finding-a-second-derivative-let-fprime-primex-be-continuous-show-that-lim-_h-rightarrow-0-fracfxh-2-

Question

Finding a Second Derivative Let $f^{\prime \prime}(x)$ be continuous. Show that
$\lim _{h \rightarrow 0} \frac{f(x+h)-2 f(x)+f(x-h)}{h^{2}}=f^{\prime \prime}(x)$

Fuzail Shakir · Accepted Answer

All right. So by direct substitution limit is determined to re getting it zero divided by zero, which is an indeterminant form. So therefore we can use low petals rule and we&#x27;re also going to use the change roles we have to limit as h approaches zero off f crime every sometimes and we have f crime of X plus Age times one minus zero plus f prime off X minus H times negative one all divided by two h So this is equal Thio prime off X plus H minus F crime off X minus H hull divided by to age. Now we tried to wreck substitution again. We&#x27;re gonna get zero over zero, which is again an indeterminant form. So if we do Moby tell through again, we&#x27;re gonna get a double prime of X plus H plus f double prime of X minus age, all divided by two. Now we try and direct substitution. You get to find a living we&#x27;re gonna get This is equal to F double prime off X

Linh Vu · Answer

it off. Experts lunch honest you f thanks plus half under X minus. So they&#x27;re not distant X. Your Jews their own would have found the, uh this will be the f X minus two f x f x and you go to zero then would you funded by zero. Therefore, we&#x27;re gonna blinding them within rule now and by the Lobaton Roma generally with after just years, there are. And now on the top, we will have no Bram Mamba experts aren&#x27;t and by the general attempts one and then minus here they understood we have zero here. So this time we could hit zero plus the from under X minus front on by the general manager Thames Manasquan here and now on the bottom one handed to us here Way simplified and we get a cogent limit. Under our best user, all every frame on the experts aren&#x27;t. And now, plus that e minor. The cancel X minus are just dividing by too much here, recording from, uh, from grow from 55 we have This will be the definition off the epigram off the X So therefore we have this limit here Equity the F number from off X

Amrita Bhasin · Answer

we know that we can rewrite this limit as H A purchase. Zero. That&#x27;s a crime. Expose Age miss off prime X minus age times Negative one, which is of prime of acts, cause extra zeros. Just acts plus f from of acts because X minus zero is also just acts divide by two, which gives us off prime of acts because two F products over two is just one F part of X. Okay, now we know that we can differentiate with respect to H instead of acts we have B is negative, too.

Darshan Maheshwari · Answer

strong global problem. 78. So we have in the part it. But the function is Jonas Xer Square. I&#x27;m here is for the part it&#x27;s and using the basic definition or better, you have to prove dark de or de itself. We have to find that sick about your deal with the eggs off ethics. Using the basic definition, this will be will do number gesturing toward 04 express EJ minus effects over rich. So I thought, express its will be replace x by explosive. So we have expressed edge pools where times he leads to the Border Express. Such minus FX is extra square. I&#x27;m here is to the parts Aurich limit just tending towards you. Records open of the brackets here. So we have women exchanging words here as a witness will be extra square. Plus, it&#x27;s square first, two X edge on distant can be needed enough years to the border extremes. He leads to the porridge minus X squared evenings to the boxes as a porridge against a. This evening is to the body. It&#x27;s out. So we have. Heat is to the products can be written upside the limit because limiters are edge So it is to the Bar. X does not have anything to do with the limits on the rest of the terms. That excess where plus sized square a stew X edge here is to the college minus X squared over Ridge, where we&#x27;re here. We have a limit, eh? Just training for What&#x27;s Syria? So this is what is asked in the park one to prove. So this is part one on in the next part. They are asking us to manage bullet. Just limit, which we get in the park, which we got in the party we owe prove that every precious is equal to something which is given on the question. OK, so this is the basics. So let&#x27;s related, Blashek says. Here is to the parks. No, let&#x27;s open up this bracket. So we have limited standing with zeros. Lassiter&#x27;s So we have extra square times. Here is to the college. Let&#x27;s it square. Tank leaders to the porridge was too x each time he leads to the porridge minus X squared porridge. Order Just reading this as the markets tune in to what&#x27;s here is that this can be deterred on us extra square eaters to the porridge minus six square. Destro on the strong, isn&#x27;t it? What Inch? Les Noble. Right in these two domes, one by one. So we have it. Square eighties to the borage overage. And then we have two X h. Here&#x27;s to the porridge. Porridge. All right, so this edges cancer, but not just cancer. From here on, this can be digitalized. Ease to the vortex limit. Just tending towards zero. We have excluded state oversight. So we have Heat is to the borders. Magnus on a bridge, we have X strangely leads to the porridge. A stew. X et is to the bullets from here. All right, Now, let&#x27;s put the limit as a sex trending towards you. So this particular Tom will be one. So we have this extra square times one. Then we have zeros. Will be zero on it. Zero. So he raised the bar. Zero. That&#x27;s nothing. But so here we have beatings to the vortex, which you mean Taniperlas. Here we have extra square, and this will be for weeks, Mrs. You know, the system weights. So this would be the required that ever do, which is actually given an army. So we have proved that Clark Bs

Amy Jiang · Answer

Okay, so we want to solve for falling limits. So let&#x27;s start by finding, if evaluated are to close. H. So we have a two plus h squared, plus an X and plus one. So this is equal to four plus for age plus H. And then, actually, this is a two plus h crack, and then we have it squared plus two plus h and M plus one. So let&#x27;s simplify that. We could have eight squared plus a five h and then plus a for 567 Okay, so we have that. The Limits As H approaches Earl of it&#x27;s squared plus five h plus seven minus f evaluated up to. That&#x27;s a four plus two plus one. So it&#x27;s 4567 all over H. Well, we can cancel out our seventh and now we see that weekend factor out of H from our new media. Now let&#x27;s use drugs, UB. So we see that our limit value is equal to 15

Jimmy Yao · Answer

great. Uh, so using the technician, that is the of the TX X two there X square into the X power. So this will you go to that? They met edge towards zero. So that is over age. So it is. It does too square you to the X plus edge miners X square into the X, and we&#x27;re going to manipulates this change. And this turn is actually equal to the limit. Edge goes to zero h. And here is X square plus two paychecks because it&#x27;s square and the e to the X plus H minus X where e to the X right. So we can catch out each of the X in the very beginning. Each of the X and limits H 20 in here when we fact out to eat to the X each the x here. So there&#x27;s things live here. Lives here is X to the X where two hx does a square e to the edge minus x square. So here Shh! Right. And this turn is actually the terms we want to prove. So we finish the eight, and now we&#x27;re going to finish the second step problem. So this is for the for the A and now we&#x27;re going to finish the second step province. Yeah, For the second problems, it can be a little bit trickier. So we have to manipulate system. So So this is a church goes to zero in the first time. It is X square into the edge. So in the two into 22 hx e to the edge endure square you to the edge, minus x square, So edge. So we&#x27;re going to combine this turn in distance together. So we have e to the X and the limit it to zero. And for this turn, it is e to the H minus one over each time X square, right. And the 2nd 10 is e to the edge limit and towards zero that is to h E to the this one over edge. The next one is into the X limit. It&#x27;s 20 and there it square you to the edge over edge. So we&#x27;re going to handle this one by one. So using the hints, we know things. 10. So, yeah, this term the limit is actually one. So the first time is going to give you x you to the X Time X Square and for the second time here. So this Kansas with this and when EJ tends to zero and distance will give you each to the X and the two X because you to the edge. When So Because this time, when h tends to zero. So this is one and the for the last time. Since it&#x27;s in there, it&#x27;s just second order. So when we cancels one change at 10 0, this one, we&#x27;ll give you zero. So we close our answer. So the answer is e to the x time X square plus two x okay.

Problem

Evaluating a Limit Consider the limit $\lim _{x \…

Problem 108 Hard Difficulty

Finding a Second Derivative Let $f^{\prime \prime}(x)$ be continuous. Show that
$\lim _{h \rightarrow 0} \frac{f(x+h)-2 f(x)+f(x-h)}{h^{2}}=f^{\prime \prime}(x)$

Answer

Using L'Hospital's Rule, we can prove the proposition.

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Ron Larson

Calculus of a Single Variable

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Anna Marie V.

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Precalculus Review - Intro

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Using L'Hospital's Rule, we can prove the proposition.

Calculus of a Single Variable

Grace H.

Anna Marie V.

Caleb E.

Kristen K.

Precalculus Review - Intro

Functions on the Real Line - Overview

Ron LarsonCalculus of a Single Variable

Grace H.

Anna Marie V.

Caleb E.

Kristen K.

Ron Larson

Calculus of a Single Variable