Problem

Find the limit. Use l'Hospital's Rule where appro…

03:27

Problem 16 Easy Difficulty

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.
$\lim _{x \rightarrow 0} \frac{\cos m x-\cos n x}{x^{2}}$

Answer

$\frac{n^{2}-m^{2}}{2}$

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Chapter 4

Applications of Derivatives

Section 3

L'Hospital's Rule: Comparing Rates of Growth

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Video Transcript

So you have, uh, the limit. Eggs exposed to cereal. Off the version. Go sign off. M X rooms. Them eggs minus co. Sign off in X over X squared. So if you were just a plugging thanks. For example, zero while on help You have co sign of zero. She's, uh, one again. Because I know zero, which is one would have wanted was one. Oh, well, good to see you. Well, so these would be above the former. Oh, issue over zero. So here we can apply love it'll do. You have, uh, farms your cereal. Also me this value to apply. Love you, Bill. Well, tell. So you differentiate the top So people to believe it. Six goes to zero. Sign off Max with the school song Go and fix, but differentiated Well, we're they got evil squared So we go ahead and complete those there That is so they're the wolf call sign is some minus sign. So why go sign up the same thing off, Max? But here you have to be careful that there's a you're Foshan and X So by the general is you know that times, you know, duty over mix which is just on on the wall here. The same story, that better, you know. So minus minus my nurse, my must sign X over two times X visibility, but squared. So here it was, uh, you definitely need a six course this year. Well, uh, some of these m times. Sino Zoo zero minus minus. Sign zero. But it's gonna be, you know, but no serial, which is Cyril. Shut up. I'm a bottom. Well, it's zero. So we gave you forms. You over is you. You cannot play well, we go again. Well, you tell I'm being that well, the friendship that again. But first, it is very super if isil minus minus is a plus, so this part would be plus in bones. Signing Vicks on the spot here would be minus on. Signed off, X sign off Unix. Look at the end there. My name's Sam Signed off and necks. So when we go ahead on the friendship, those two Oh, what you step on it. They love my no signs minus co sign minus Ann Co Sign off. You see, Martin, don't mix, but times the negative off M X, which is m so that minus co signed off him. Extend him. Plus, in times there are the go sign off. Next, it's gonna be call sign X, But times that you're direct looks. So here, Sam comes from the energy of X from irritable connects we're gonna get and and then that divided by the book to ex juice too. So that simplify, it is gonna be They go to war. Forget words that were a little bit. It's also the luminous ex goes to zero minus AM squared. No sign of the Mets plus and squared question of opinion squared this sign up looks or two Great being a well, at this point, these value too, Levin, huh? It's zero. So because 40 it will go to percent. Zero year, we'll go. So because I have zero, which weren't is gonna be that holding it will be equal to minus m squared plus and squirt. Oh, you like to um so she'd be finer putting there. Here on from Began a square My guess I'm square divided by two. So as you see here, we have to apply love. Go Look. The whole place was here. There. You're gonna play a little as many times as you want. That's long that I see, you know, just steps. Just that expression, which indeed, in this case, So you you have the answer is gonna be And the square of making same square, right?

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