Calculus Essay - 576 Words

Calculus One of the greatest contributions to modern mathematics, science, and engineering was the invention of calculus near the end of the 17th century, says The New Book of Popular Science. Without the invention of calculus, many technological accomplishments, such as the landing on the moon, would have been difficult. The word calculus originated from the Latin word meaning pebble. This is probably because people many years ago used pebbles to count and do arithmetic problems. The two people with an enormous contribution to the discovery of the theorems of calculus were Sir Isaac Newton of England and Baron Gottfried Wilhelm of Germany. They discovered these theorems during the 17th century within a few years of†¦show more content†¦In economics and business there are some uses for calculus. One important application of integral calculus in business is the evaluation of the area under a function. This can be used in a probability model. Probability is another uses in integral calculus for business because you could find how often something will appear in a certain range in a certain time. A function used for probability in uniform distribution. The function is f(x) = 1 (b - a) for a x = b. Some economics uses is figuring marginal and total cost. The function is TC = {MC = TVC + FC. Another is the demand on a sales product. ex. Demand on Beer that brings in different variables to see how the consumption of beer is. The function is a multivariate function f(m, p, r, s) = (1.058)(m^.136)(p^- .727)(r^.914)(s^.816) where m = aggregate real income : p = average retail price of beer r = average retail price level of all other consumer goods s = measure of strength of beer (how consumers like it) as you can see if everything but r stays constant then the demand will go up. Some terms used in calculus frequently used to learn you need to know what they are. Derivative is the fundamental concept of calculus that is how things change. (ex. instantaneous velocity) Functions are always used in all applications. A function is an equation with one or more variables where only one x value will produce only one y value is a function. Also you will need to learn and memorizeShow MoreRelatedHistory of Calculus Essay1186 Words   |  5 PagesHistory of Calculus The history of calculus falls into several distinct time periods, most notably the ancient, medieval, and modern periods. The ancient period introduced some of the ideas of integral calculus, but does not seem to have developed these ideas in a rigorous or systematic way. Calculating volumes and areas, the basic function of integral calculus, can be traced back to the Egyptian Moscow papyrus (c. 1800 BC), in which an Egyptian successfully calculated the volume of a pyramidalRead MoreCalculus2140 Words   |  9 Pages1. ht= -4.9t2+ 450, where t is the time elapsed in seconds and h is the height in metres. a) Table of Values t(s) | h(t) (m) | 0 | ht= -4.9(0)2+ 450= 450 | 1 | ht= -4.9(1)2+ 450= 445.1 | 2 | ht= -4.9(2)2+ 450= 430.4 | 3 | ht= -4.9(3)2+ 450= 405.9 | 4 | ht= -4.9(4)2+ 450=371.6 | 5 | ht= -4.9(5)2+ 450=327.5 | 6 | ht= -4.9(6)2+ 450= 273.6 | 7 | ht= -4.9(7)2+ 450= 209.9 | 8 | ht= -4.9(8)2+ 450= 136.4 | 9 | ht= -4.9(9)2+ 450=53.1 | 10 | ht= -4.9(10)2+ 450= -40 | Read MoreEudoxus Contribution to Calculus550 Words   |  2 Pagesmathematician and astronomer of ancient times, particularly 408 – 355 BC. He lived in Greece and studied under Plato, one of the most notable philosophers ever. In Calculus, Eudoxus is known for advancing Antiphon’s ideas on the method of exhaustion. The method of exhaustion is very important to calculus because one of the fundamental themes of calculus is sending variables (or whatever it happens to be) to infinity, which is a branch of the method of exhaustion. This is known as taking the limit. EudoxusRead MoreEssay on The Evolution of Differential Calculus2658 Words   |  11 PagesDifferential calculus is a subfield of Calculus that focuses on derivates, which are used to describe rates of change that are not constants. The term ‘differential’ comes from the process known as differentiation, which is the process of finding the derivative of a curve. Differential calculus is a major topic covered in calculus. According to Interactive Mathematics, â€Å"We use the derivative to determine the maximum and minimum values of particular functions (e.g. cost, strength, amount of materialRead MoreAp Calculus Ab Topic Is Solving Limits986 Words   |  4 PagesMy favorite AP Calculus AB topic is solving limits. This is because limits are fairly simple to solve. AP Calculus AB was extremely difficult for me, so I was happy to find a topic that was somewhat easy for me to understand. I know that a limit is the value that a function or sequence approaches as the input or index approaches some x-value. To solve most limits, I had to use six basic properties of limits: the sum rule, the difference rule, the product rule, the constant multiple rule, the quotientRead MoreCalculus As A Part Of Modern Mathematics Education1708 Words   |  7 PagesCalculus (from Latin calculus, literally small pebble used for counting)[1] is the mathematical study of change, in the same way that geometry is the study of shape and algebra is the study of operations and their application to solving equations. It has two major branches, differential calculus (concerning rates of change and slopes of curves),[2] and integral calculus (concerning accumulation of quantities and the areas under and between curves);[3] these two branches are related to each otherRead MoreDerivative Is A Complex Subject Of Calculus2802 Words   |  12 PagesDerivative is a complex subject of calculus. In calculus, derivative is a key term developed by both Newton and Leibniz. With function f (t), the first derivative is defined asf^ (t)= df/dt= limâ” ¬(h→0)⠁ ¡Ã£â‚¬â€"(f(t)-f(t-h))/hã€â€". There is also a second derivative known as second-order derivative. The second-order derivative is defined: f^ (t)= (d^2 f)/(dt^2 )= limâ” ¬(h→0)⠁ ¡Ã£â‚¬â€"(f^ (t)-f^ (t-h))/hã€â€" =limâ” ¬(h→0)⠁ ¡Ã£â‚¬â€"1/h {(f(t)-f(t-h))/h- (f(t-h)-f(t-2h))/h}ã€â€" =limâ” ¬(h→0)⠁ ¡Ã£â‚¬â€"(f(t)-2f(t-h)+f(t-2h))/h^2 ã€â€" (PodlubnyRead MoreAnalyble Themes In The Calculus Diaries By Jennifer Ouellette978 Words   |  4 PagesThe author of The Calculus Diaries, Jennifer Ouellette, conveys a story to the reader that calculus isn’t as evil as everyone makes it seem, and to show its uses in everyday life. This happens expertly by using relatable topics such as gambling in Vegas, how to lose weight, and how to survive the zombie apocalypse. Ouellette makes it a key point that anyone can understand and apply calculus, even those who dread even hearing the term. 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Happen without one notice that they are actually applied it when they do some worksRead MoreCalculus C Are Largely Defined By Derivatives Of Vector Valued And Parametrically Defined Function965 Words   |  4 PagesThe major topics explored in Calculus C are largely defined by derivatives of vector-valued and parametrically defined functions, integration by partial fractions, improper integrals, series convergence (Taylor and Maclaurin), L’Hopitals Rule, and numerous applications. All of the following topics require a solid foundation in not only Calculus A but also Calculus B. Vector-valued functions include mathematical functions of one or more variables whose range is defined as a set of both multidimensional

The Twilight Saga 4 Breaking Dawn 17. What Do I Look Like … Free Essays

17. What Do I Look Like? The Wizard Of Oz? You Need A Brain? You Need A Heart? Go Ahead.Take Mine. We will write a custom essay sample on The Twilight Saga 4: Breaking Dawn 17. What Do I Look Like? †¦ or any similar topic only for you Order Now Take Everything I Have. HEART? GO AHEAD. TAKE MINE. TAKE EVERYTHING I HAVE. I sort of had a plan as I ran to the Cullens’ garage. The second part of it was totaling the bloodsucker’s car on my way back. So I was at a loss when I mashed the button on the keyless remote, and it was not his Volvo that beeped and flashed its lights for me. It was another car – a standout even in the long line of vehicles that were mostly all drool-worthy in their own ways. Did he actually mean to give me the keys to an Aston Martin Vanquish, or was that an accident? I didn’t pause to think about it, or if this would change that second part of my plan. I just threw myself into the silky leather seat and cranked the engine while my knees were still crunched up under the steering wheel. The sound of the motor’s purr might have made me moan another day, but right now it was all I could do to concentrate enough to put it in drive. I found the seat release and shoved myself back as my foot rammed the pedal down. The car felt almost airborne as it leaped forward. It only took seconds to race through the tight, winding drive. The car responded to me like my thoughts were steering rather than my hands. As I blew out of the green tunnel and onto the highway, I caught a fleeting glimpse of Leah’s gray face peering uneasily through the ferns. For half a second, I wondered what she’d think, and then I realized that I didn’t care. I turned south, because I had no patience today for ferries or traffic or anything else that meant I might have to lift my foot off the pedal. In a sick way, it was my lucky day. If by lucky you meant taking a well-traveled highway at two hundred without so much as seeing one cop, even in the thirty-mile-an-hour speed-trap towns. What a letdown. A little chase action might have been nice, not to mention that the license plate info would bring the heat down on the leech. Sure, he’d buy his way out of it, but it might have been just a little inconvenient for him. The only sign of surveillance i came across was just a hint of dark brown fur flitting through the woods, running parallel to me for a few miles on the south side of Forks. Quil, it looked like. He must have seen me, too, because he disappeared after a minute without raising an alarm. Again, I almost wondered what his story would be before I remembered that I didn’t care. I raced around the long U-shaped highway, heading for the biggest city I could find. That was the first part of my plan. It seemed to take forever, probably because I was still on the razor blades, but it actually didn’t even take two hours before I was driving north into the undefined sprawl that was part Tacoma and part Seattle. I slowed down then, because I really wasn’t trying to kill any innocent bystanders. This was a stupid plan. It wasn’t going to work. But, as I’d searched my head for any way at all to get away from the pain, what Leah’d said today had popped in there. That would go away, you know, if you imprinted. You wouldn’t have to hurt over her anymore. Seemed like maybe getting your choices taken away from you wasn’t the very worst thing in the world. Maybe feeling like this was the very worst thing in the world. But I’d seen all the girls in La Push and up on the Makah rez and in Forks. I needed a wider hunting range. So how do you look for a random soul mate in a crowd? Well, first, I needed a crowd. So I tooled around, looking for a likely spot. I passed a couple of malls, which probably would’ve been pretty good places to find girls my age, but I couldn’t make myself stop. Did I want to imprint on some girl who hung out in a mall all day? I kept going north, and it got more and more crowded. Eventually, I found a big park full of kids and families and skateboards and bikes and kites and picnics and the whole bit. I hadn’t noticed till now – it was a nice day. Sun and all that. People were out celebrating the blue sky. I parked across two handicapped spots – just begging for a ticket – and joined the crowd. I walked around for what felt like hours. Long enough that the sun changed sides in the sky. I stared into the face of every girl who passed anywhere near me, making myself really look, noticing who was pretty and who had blue eyes and who looked good in braces and who had way too much makeup on. I tried to find something interesting about each face, so that I would know for sure that I’d really tried. Things like: This one had a really straight nose; that one should pull her hair out of her eyes; this one could do lipstick ads if the rest of her face was as perfect as her mouth___ Sometimes they stared back. Sometimes they looked scared – like they were thinking, Who is this big freak glaring at me? Sometimes I thought they looked kind of interested, but maybe that was just my ego running wild. Either way, nothing. Even when I met the eyes of the girl who was – no contest – the hottest girl in the park and probably in the city, and she stared right back with a speculation that looked like interest, I felt nothing. Just the same desperate drive to find a way out of the pain. As time went on, I started noticing all the wrong things. Bella things. This one’s hair was the same color. That one’s eyes were sort of shaped the same. This one’s cheekbones cut across her face in just the same way. That one had the same little crease between her eyes – which made me wonder what she was worrying about___ That was when I gave up. Because it was beyond stupid to think that I had picked exactly the right place and time and I was going to simply walk into my soul mate just because I was so desperate to. It wouldn’t make sense to find her here, anyway. If Sam was right, the best place to find my genetic match would be in La Push. And, clearly, no one there fit the bill. If Billy was right, then who knew? What made for a stronger wolf? I wandered back to the car and then slumped against the hood and played with the keys. Maybe I was what Leah thought she was. Some kind of dead end that shouldn’t be passed on to another generation. Or maybe it was just that my life was a big, cruel joke, and there was no escape from the punch line. â€Å"Hey, you okay? Hello? You there, with the stolen car.† It took me a second to realize that the voice was talking to me, and then another second to decide to raise my head. A familiar-looking girl was staring at me, her expression kind of anxious. I knew why I recognized her face – I’d already catalogued this one. Light red-gold hair, fair skin, a few gold-colored freckles sprinkled across her cheeks and nose, and eyes the color of cinnamon. â€Å"If you’re feeling that remorseful over boosting the car,† she said, smiling so that a dimple popped out in her chin, â€Å"you could always turn yourself in.† â€Å"It’s borrowed, not stolen,† I snapped. My voice sounded horrible – like I’d been crying or something. Embarrassing. â€Å"Sure, thatW hold up in court.† I glowered. â€Å"You need something?† â€Å"Not really. I was kidding about the car, you know. It’s just that†¦ you look really upset about something. Oh, hey, I’m Lizzie.† She held out her hand. I looked at it until she let it fall. â€Å"Anyway†¦,† she said awkwardly, â€Å"I was just wondering if I could help. Seemed like you were looking for someone before.† She gestured toward the park and shrugged. â€Å"Yeah.† She waited. I sighed. â€Å"I don’t need any help. She’s not here.† â€Å"Oh. Sorry.† â€Å"Me, too,† I muttered. I looked at the girl again. Lizzie. She was pretty. Nice enough to try to help a grouchy stranger who must seem nuts. Why couldn’t she be the one? Why did everything have to be so freaking complicated? Nice girl, pretty, and sort of funny. Why not? â€Å"This is a beautiful car,† she said. â€Å"It’s really a shame they’re not making them anymore. I mean, the Vantage’s body styling is gorgeous, too, but there’s just something about the Vanquish___† Nice girl who knew cars. Wow. I stared at her face harder, wishing I knew how to make it work. C’mon, Jake – imprint already. â€Å"How’s it drive?† she asked. â€Å"Like you wouldn’t believe,† I told her. She grinned her one-dimple smile, clearly pleased to have dragged a halfway civil response out of me, and I gave her a reluctant smile back. But her smile did nothing about the sharp, cutting blades that raked up and down my body. No matter how much I wanted it to, my life was not going to come together like that. I wasn’t in that healthier place where Leah was headed. I wasn’t going to be able to fall in love like a normal person. Not when I was bleeding over someone else. Maybe – if it was ten years from now and Bella’s heart was long dead and I’d hauled myself through the whole grieving process and come out in one piece again – maybe then I could offer Lizzie a ride in a fast car and talk makes and models and get to know something about her and see if I liked her as a person. But that wasn’t going to happen now. Magic wasn’t going to save me. I was just going to have to take the torture like a man. Suck it up. Lizzie waited, maybe hoping I was going to offer her that ride. Or maybe not. â€Å"I’d better get this car back to the guy I borrowed it from,† I muttered. She smiled again. â€Å"Glad to hear you’re going straight.† â€Å"Yeah, you convinced me.† She watched me get in the car, still sort of concerned. I probably looked like someone who was about to drive off a cliff. Which maybe I would’ve, if that kind of move’d work for a werewolf. She waved once, her eyes trailing after the car. At first, I drove more sanely on the way back. I wasn’t in a rush. I didn’t want to go where I was going. Back to that house, back to that forest. Back to the pain I’d run from. Back to being absolutely alone with it. Okay, that was melodramatic. I wouldn’t be all alone, but that was a bad thing. Leah and Seth would have to suffer with me. I was glad Seth wouldn’t have to suffer long. Kid didn’t deserve to have his peace of mind ruined. Leah didn’t, either, but at least it was something she understood. Nothing new about pain for Leah. I sighed big as I thought about what Leah wanted from me, because I knew now that she was going to get it. I was still pissed at her, but I couldn’t ignore the fact that i could make her life easier. And – now that I knew her better – I thought she would probably do this for me, if our positions were reversed. It would be interesting, at the very least, and strange, too, to have Leah as a companion – as a friend. We were going to get under each other’s skin a lot, that was for sure. She wouldn’t be one to let me wallow, but I thought that was a good thing. I’d probably need someone to kick my butt now and then. But when it came right down to it, she was really the only friend who had any chance of understanding what I was going through now. I thought of the hunt this morning, and how close our minds had been for that one moment in time. It hadn’t been a bad thing. Different. A little scary, a little awkward. But also nice in a weird way. I didn’t have to be all alone. And I knew Leah was strong enough to face with me the months that were coming. Months and years. It made me tired to think about it. I felt like I was staring out across an ocean that I was going to have to swim from shore to shore before I could rest again. So much time coming, and then so little time before it started. Before I was flung into that ocean. Three and a half more days, and here I was, wasting that little bit of time I had. I started driving too fast again. I saw Sam and Jared, one on either side of the road like sentinels, as I raced up the road toward Forks. They were well hidden in the thick branches, but I was expecting them, and I knew what to look for. I nodded as I blew past them, not bothering to wonder what they made of my day trip. I nodded to Leah and Seth, too, as I cruised up the Cullens’ driveway. It was starting to get dark, and the clouds were thick on this side of the sound, but I saw their eyes glitter in the glow of the headlights. I would explain to them later. There’d be plenty of time for that. It was a surprise to find Edward waiting for me in the garage. I hadn’t seen him away from Bella in days. I could tell from his face that nothing bad had happened to her. In fact, he looked more peaceful than before. My stomach tightened as I remembered where that peace came from. It was too bad that – with all my brooding – I’d forgotten to wreck the car. Oh well. I probably wouldn’t have been able to stand hurting this car, anyway. Maybe he’d guessed as much, and that’s why he’d lent it to me in the first place. â€Å"A few things, Jacob,† he said as soon as I cut the engine. I took a deep breath and held it for a minute. Then, slowly, I got out of the car and threw the keys to him. â€Å"Thanks for the loan,† I said sourly. Apparently, it would have to be repaid. â€Å"What do you want now?† â€Å"Firstly†¦ I know how averse you are to using your authority with your pack, but†¦Ã¢â‚¬  I blinked, astonished that he would even dream of starting in on this one. â€Å"What?† â€Å"If you can’t or won’t control Leah, then I – â€Å" â€Å"Leah?† I interrupted, speaking through my teeth. â€Å"What happened?† Edward’s face was hard. â€Å"She came up to see why you’d left so abruptly. I tried to explain. I suppose it might not have come out right.† â€Å"What did she do?† â€Å"She phased to her human form and – â€Å" â€Å"Really?† I interrupted again, shocked this time. I couldn’t process that. Leah letting her guard down right in the mouth of the enemy’s lair? â€Å"She wanted to†¦ speak to Bella.† â€Å"To Bella?† Edward got all hissy then. â€Å"I won’t let Bella be upset like that again. I don’t care how justified Leah thinks she is! I didn’t hurt her – of course I wouldn’t – but I’ll throw her out of the house if it happens again. I’ll launch her right across the river – â€Å" â€Å"Hold on. What did she say?† None of this was making any sense. Edward took a deep breath, composing himself. â€Å"Leah was unnecessarily harsh. I’m not going to pretend that I understand why Bella is unable to let go of you, but I do know that she does not behave this way to hurt you. She suffers a great deal over the pain she’s inflicting on you, and on me, by asking you to stay. What Leah said was uncalled for. Bella’s been crying – â€Å" â€Å"Wait – Leah was yelling at Bella about me?† He nodded one sharp nod. â€Å"You were quite vehemently championed.† Whoa. â€Å"I didn’t ask her to do that.† â€Å"I know.† I rolled my eyes. Of course he knew. He knew everything. But that was really something about Leah. Who would have believed it? Leah walking into the bloodsuckers’ place human to complain about how /was being treated. â€Å"I can’t promise to control Leah,† I told him. â€Å"I won’t do that. But I’ll talk to her, okay? And I don’t think there’ll be a repeat. Leah’s not one to hold back, so she probably got it all off her chest today.† â€Å"I would say so.† â€Å"Anyway, I’ll talk to Bella about it, too. She doesn’t need to feel bad. This one’s on me.† â€Å"I already told her that.† â€Å"Of course you did. Is she okay?† â€Å"She’s sleeping now. Rose is with her.† So the psycho was â€Å"Rose† now. He’d completely crossed over to the dark side. He ignored that thought, continuing with a more complete answer to my question. â€Å"She’s†¦ better in some ways. Aside from Leah’s tirade and the resulting guilt.† Better. Because Edward was hearing the monster and everything was all lovey-dovey now. Fantastic. â€Å"It’s a bit more than that,† he murmured. â€Å"Now that I can make out the child’s thoughts, it’s apparent that he or she has remarkably developed mental facilities. He can understand us, to an extent.† My mouth fell open. â€Å"Are you serious?† â€Å"Yes. He seems to have a vague sense of what hurts her now. He’s trying to avoid that, as much as possible. He†¦ loves her. Already.† I stared at Edward, feeling sort of like my eyes might pop out of their sockets. Underneath that disbelief, I could see right away that this was the critical factor. This was what had changed Edward – that the monster had convinced him of this love. He couldn’t hate what loved Bella. It was probably why he couldn’t hate me, either. There was a big difference, though. I wasn’t killing her. Edward went on, acting like he hadn’t heard all that. â€Å"The progress, I believe, is more than we’d judged. When Carlisle returns – â€Å" â€Å"They’re not back?† I cut in sharply. I thought of Sam and Jared, watching the road. Would they get curious as to what was going on? â€Å"Alice and Jasper are. Carlisle sent all the blood he was able to acquire, but it wasn’t as much as he was hoping for – Bella will use up this supply in another day the way her appetite has grown. Carlisle stayed to try another source. I don’t think that’s necessary now, but he wants to be covered for any eventuality.† â€Å"Why isn’t it necessary? If she needs more?† I could tell he was watching and listening to my reaction carefully as he explained. Tm trying to persuade Carlisle to deliver the baby as soon as he is back.† â€Å"What?† â€Å"The child seems to be attempting to avoid rough movements, but it’s difficult. He’s become too big. It’s madness to wait, when he’s clearly developed beyond what Carlisle had guessed. Bella’s too fragile to delay.† I kept getting my legs knocked out from under me. First, counting on Edward’s hatred of the thing so much. Now, I’d realized that I thought of those four days as a sure thing. I’d banked on them. The endless ocean of grief that waited stretched out before me. I tried to catch my breath. Edward waited. I stared at his face while I recovered, recognizing another change there. â€Å"You think she’s going to make it,† I whispered. â€Å"Yes. That was the other thing I wanted to talk to you about.† I couldn’t say anything. After a minute, he went on. â€Å"Yes,† he said again. â€Å"Waiting, as we have been, for the child to be ready, that was insanely dangerous. At any moment it could have been too late. But if we’re proactive about this, if we act quickly, I see no reason why it should not go well. Knowing the child’s mind is unbelievably helpful. Thankfully, Bella and Rose agree with me. Now that I’ve convinced them it’s safe for the child if we proceed, there’s nothing to keep this from working.† â€Å"When will Carlisle be back?† I asked, still whispering. I hadn’t got my breath back yet. â€Å"By noon tomorrow.† My knees buckled. I had to grab the car to hold myself up. Edward reached out like he was offering support, but then he thought better of it and dropped his hands. â€Å"I’m sorry,† he whispered. â€Å"I am truly sorry for the pain this causes you, Jacob. Though you hate me, I must admit that I don’t feel the same about you. I think of you as a†¦ a brother in many ways. A comrade in arms, at the very least. I regret your suffering more than you realize. But Bella is going to survive† – when he said that his voice was fierce, even violent – â€Å"and I know that’s what really matters to you.† He was probably right. It was hard to tell. My head was spinning. â€Å"So I hate to do this now, while you’re already dealing with too much, but, clearly, there is little time. I have to ask you for something – to beg, if I must.† â€Å"I don’t have anything left,† I choked out. He lifted his hand again, as if to put it on my shoulder, but then let it drop like before and sighed. â€Å"I know how much you have given,† he said quietly. â€Å"But this is something you do have, and only you. I’m asking this of the true Alpha, Jacob. I’m asking this of Ephraim’s heir.† I was way past being able to respond. â€Å"I want your permission to deviate from what we agreed to in our treaty with Ephraim. I want you to grant us an exception. I want your permission to save her life. You know 111 do it anyway, but I don’t want to break faith with you if there is any way to avoid it. We never intended to go back on our word, and we don’t do it lightly now. I want your understanding, Jacob, because you know exactly why we do this. I want the alliance between our families to survive when this is over.† I tried to swallow. Sam, I thought. It’s Sam you want. â€Å"No. Sam’s authority is assumed. It belongs to you. You’ll never take it from him, but no one can rightfully agree to what I’m asking except for you† It’s not my decision. â€Å"It is, Jacob, and you know it. Your word on this will condemn us or absolve us. Only you can give this to me.† can’t think. I don’t know. â€Å"We don’t have much time.† He glanced back toward the house. No, there was no time. My few days had become a few hours. don’t know. Let me think. Just give me a minute here, okay? â€Å"Yes.† I started walking to the house, and he followed. Crazy how easy it was, walking through the dark with a vampire right beside me. It didn’t feel unsafe, or even uncomfortable, really. It felt like walking next to anybody. Well, anybody who smelled bad. There was a movement in the brush at the edge of the big lawn, and then a low whimper. Seth shrugged through the ferns and loped over to us. â€Å"Hey, kid,† I muttered. He dipped his head, and I patted his shoulder. â€Å"S’all cool,† I lied. â€Å"I’ll tell you about it later. Sorry to take off on you like that.† He grinned at me. â€Å"Hey, tell your sister to back off now, okay? Enough.† Seth nodded once. I shoved against his shoulder this time. â€Å"Get back to work. I’ll spell you in a bit.† Seth leaned against me, shoving back, and then he galloped into the trees. â€Å"He has one of the purest, sincerest, kindest minds I’ve ever heard,† Edward murmured when he was outof sight. â€Å"You’re lucky to have his thoughts to share.† â€Å"I know that,†! grunted. We started toward the house, and both of our heads snapped up when we heard the sound of someone sucking through a straw. Edward was in a hurry then.He darted up the porch stairs and was gone. â€Å"Bella, love, Ithought you were sleeping,† I heard him say. â€Å"I’m sorry, I wouldn’t have left.† â€Å"Don’t worry. Ijust got so thirsty – it woke me up.It’s a good thing Carlisle is bringing more. This kid is going to need it when he gets out of me.† â€Å"True. That’s a good point.† â€Å"I wonder if he’ll want anything else,† she mused. â€Å"I suppose we’ll find out.† I walked through the door. Alice said, â€Å"Finally,† and Bella’s eyes flashed to me. That infuriating, irresistible smile broke across her face for one second. Then it faltered, and her face fell. Her lips puckered, like she was trying not to cry. I wanted to punch Leah right in her stupid mouth. â€Å"Hey, Bells,† Isaid quickly. â€Å"How ya doing?† â€Å"I’m fine,† she said. â€Å"Big day today, huh? Lots of new stuff.† â€Å"You don’t have to do that, Jacob.† â€Å"Don’t know what you’re talking about,† I said, going to sit on the arm of the sofa by her head. Edward had the floor there already. She gave me a reproachful look. â€Å"I’m so s – † she started to say. I pinched her lips together between my thumb and finger. â€Å"Jake,† she mumbled, trying to pull my hand away. Her attempt was so weak it was hard to believe that she was really trying. I shook my head. â€Å"You can talk when you’re not being stupid.† â€Å"Fine,I won’t say it,† it sounded like she mumbled. I pulled my hand away. â€Å"Sorry!† she finished quickly, and then grinned. I rolledmy eyes and then smiled back at her. When I stared into her eyes, I saw everything that I’d been looking for in the park. Tomorrow, she’d be someone else. But hopefully alive, and that was what counted, right? She’d look at me with the same eyes, sort of. Smile with the same lips, almost. She’d still know me better than anyone who didn’t havefull access to the inside of my head. Leah might be an interesting companion, maybe even a true friend – someone who would stand up for me. But she wasn’t my best friend the way thatBella was. Aside from the impossible love I felt for Bella, there was also that other bond, and it ran bone deep. Tomorrow, she’d be my enemy. Or she’d be myally. And, apparently, that distinction was up to me. I sighed. Fine!I thought, giving up the very last thing i had to give. It made me feel hollow. Go ahead. Save her. As Ephraim’s heir, you have my permission, my word, that this will not violate the treaty. The others will just have to blame me. You were right – they can’t deny that it’s my right to agree to this. ‘Thank you.† Edward’s whisper was low enough that Bella didn’t hear anything. But the words were so fervent that, from the corner of my eye, I saw the other vampires turning to stare. â€Å"So,†Bella asked, working to be casual. â€Å"How was your day?† â€Å"Great. Went for a drive. Hung out in the park.† â€Å"Sounds nice.† â€Å"Sure, sure.† Suddenly, she made a face. â€Å"Rose?† she asked. I heard Blondie chuckle. â€Å"Again?† â€Å"I think I’ve drunk two gallons in the last hour,† Bella explained. Edward and I both got out of the way while Rosalie came to lift Bella from the couch and take her to the bathroom. â€Å"Can I walk?† Bella asked. â€Å"My legs are so stiff.† â€Å"Are you sure?† Edward asked. â€Å"Rose’llcatch me if I trip over my feet. Which could happen pretty easily, since I can’t see them.† Rosalie set Bellacarefully on her feet, keeping her hands right atBella’s shoulders. Bella stretched her arms out in front of her, wincing a little. â€Å"That feels good,† she sighed. â€Å"Ugh, but I’m huge.† She really was. Her stomach was its own continent. â€Å"One more day,† she said, and patted her stomach. I couldn’t help the pain that shot through me in a sudden, stabbing burst, but I tried to keep it off my face. I could hide it for one more day, right? â€Å"All righty, then. Whoops – oh, no!† The cup Bella had left on the sofa tumbled to one side, the dark red blood spilling out onto the pale fabric. Automatically, though three other hands beat her there, Bella bent over, reaching out to catch it. There was the strangest, muffled ripping sound from the center of her body. â€Å"Oh!† she gasped. And then she went totally limp, slumping toward the floor. Rosalie caught her in the same instant, before she could fall. Edward was there, too, hands out, the mess on the sofa forgotten. â€Å"Bella?† he asked, and then his eyes unfocused, and panic shot across his features. A half second later,Bella screamed. Itwas not justa scream, it was a blood-curdling shriek of agony. The horrifying sound cut off with a gurgle, and her eyes rolled back into her head. Her body twitched, arched in Rosalie’s arms, and then Bella vomited a fountain of blood. How to cite The Twilight Saga 4: Breaking Dawn 17. What Do I Look Like? †¦, Essay examples

Conversation starters Essay Example For Students

Conversation starters Essay 1 (14-ounce) can Eagle Brand Sweetened Condensed Milk1 (6-ounce) package almond brickle chips, or 6 (1 3/16-ounce) milk chocolate-covered English toffee candy bars, cut into small pieces1. Preheat oven to 375. In large bowl, combine oats,flour,peanuts, sugar, baking soda and salt; stir in margarine until crumbly. Reserving 1 1/2 cups crumb mixture, press remainder on bottom of 2. Bake 12 minutes. Meanwhile, in small mixer bowl, beat Eagle Brand with peanut butter until smooth; spread evenly over prepared crust to within 1/4 inch of edge. In medium bowl, combine reserved crumb mixture 3. Sprinkle evenly over peanut butter mixture; press down firmly. Bake 20 minutes or until golden brown. Cool. Cut into bars. Store loosely ***********************************************************************2 cups (12 ounces) semi-sweet chocolate chips1 (14-ounce) can Eagle Brand Sweetened Condensed Milk1 to 1 1/2 cups coarsely chopped walnuts1. Preheat oven to 350. In large saucepan,over low heat, m elt 1 cup chips with margarine; remove from heat. 2. Add biscuit mix, Eagle Brand, egg and vanilla. Stir nuts and remaining 1 cup chips. Turn into well-greased 139-inch baking pan. 3. Bake 20 to 25 minutes or until brownies begin to pull away from sides of pan. Cool. Sprinkle with confectioners sugar. Cut into bars. Store tightly covered at room temperature. ***************************************************************************1 (14-ounce) can Eagle Brand Sweetened Condensed Milk1. In large saucepan, combine cocoa, cinnamon and salt. Add Eagle Brand; mix until smooth. Over medium heat, slowly stir in water, coffee, brandy and rum. Heat through, stirring occasionally. Do not boil. Bibliography: