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Find the limit. Use l'Hospital's Rule where appropriate. If there is a more elementary method, consider using it. If l'Hospital's Rule doesn't apply, explain why.$\lim _{x \rightarrow 0} \frac{e^{x}-e^{-x}-2 x}{x-\sin x}$

$\lim _{x \rightarrow 0} \frac{e^{x}+e^{-x}}{\cos x}=2$

Calculus 1 / AB

Chapter 4

Applications of Derivatives

Section 3

L'Hospital's Rule: Comparing Rates of Growth

Differentiation

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So we have the myriad six. So zero off the function e the board eggs minus the minus x. Oh, lives to eggs over X minus. Sign off books. Well, so what happens if he just go ahead on play here? The place for X equals zero. So here, we're gonna get They're gonna get one of these here. It's just one issues one. So one minus one and they will to them. Zero is just you. Why, I might as one over minus zero. Over. Well, zero on the design of zero. So zero. So you're gonna get something over the farm or what does one is, you know. So you're on, Your Highness, your zero. So your orders. You, um So here we're We're in good shape, Toe. I love you, Joe. You're here. I love you, Joe. So what they don't tell us is that these need will be ableto the limit. Sex goes through. Same, please. Zero. But you different shit. They if I weren't She So there is about eating the exits. Just you did the X veritable getting mine six will be You didn't mind in six, but, uh, here we have to be careful that there is on your function there. So by the channel, you get out mind as one coming out off the function minus six. So these mind, this is what walking playing might see DDX on the Red Bull. Twix, She's still so my still I'm game home bottom here with that gettable exit. Just one. They're a team of scientists. Go sign. So one minus. Oh, son hooks. So all these simplified will be through the X. Okay. Minus minus plus minus six minus two. So well again. Well, you just blogging. X equals zero. We're going out. He is here about Swann. Plus you didn't mind. Syrup is also one. It was one minor. Still, that is your here but one minus because I'm of you is one. So again the well we perform so well. We can't go ahead on apply. You know there is no for being you. How many times you gonna buy local? So lactose is that these little people toe limit off ex going to the same place but ready one top. Where you my dear bottom. So they're atrophied. Three exits. Just x Remember here that these mind knows he wanted playing that. So that's how blasts you gonna wait? Six plus, you didn't like six. Then again from the channel rule from the minor sex there come south, another miners wander and then they would look tow this year. So my seal, then the girls wanted Cyril. That live off minus co sign is, uh, minus sign so minus sign, we'll fix so well. Here you have. You know, whole X here is going to show you your place here expletives you these side of zero zero. He's the one in that. I'm saying there because he was one minus. You did the minus here, which is one so again you would have something of the farm zero over zero. Well, you can go ahead and play love you go one time, so keep on. They're due in our game way we know to be friendship could be excessive if you're pretty, ext t x minus. You didn't wait? A six will be minus minus X multiplied by your minus one. Coming from the minor. Six. I've been here, but well, that's this is a minus on the minus of that's plus sign sign is a sign. So these accounts for there Developed they So it's the bottom? No. So at this point, it seems a very you can get something because we're dividing by something that does not go to zero, cause I know zero is one. So at this point, we come forget and focus on a zero. This one, my nose of miners who get a plus So one they did that minus plus what? It's just gonna be you go to two over one. Just one. Just resist yet. So I used to thio because he gets to apply though waas wise through. That's but we finally got a deal. Beaches step. You have to make sure that you're, you know no, leave me. That is, uh, forward for which is likely to apply locator So big toe the farm zero or zero Or security or if you

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