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If $ f' $ is continuous, use l'Hospital's Rule to show that$$ \displaystyle \lim_{h\to 0} \frac{f(x + h) - f(x - h)}{2h} = f'(x) $$Explain the meaning of this equation with the aid of a diagram.

$a=\frac{4}{3}$, $b=-2$

02:22

Wen Z.

01:18

Carson M.

Calculus 1 / AB

Calculus 2 / BC

Chapter 4

Applications of Differentiation

Section 4

Indeterminate Forms and l'Hospital's Rule

Derivatives

Differentiation

Volume

Missouri State University

University of Nottingham

Boston College

Lectures

01:11

In mathematics, integratio…

06:55

In grammar, determiners ar…

01:10

If $f^{\prime}$ is continu…

If $ f" $ is continuo…

01:50

If $f^{\prime \prime}$ is …

01:54

$$\begin{aligned}&…

02:08

Prove that $ f $ is contin…

01:19

Finding a Second Derivativ…

00:53

Find$$\lim _{h \righta…

01:15

Illustrate l'Hospital…

01:12

Find $$\lim _{h \rightarro…

Mhm. For this problem. Um Since the limit is in the indeterminate form 0/0, we'll use low Patel's rule and that's going to give us um F of X. Class H minus F of X minus H. All over to H. Um And since we're applying the limit as H goes to zero, what we end up getting is when we take the derivative, since we can't do that, we're going to get F prime have expressed H I'm 1 uh-. That's gonna be, we're gonna multiply that by negative one. Eventually it'll be plus after prime of X minus H. And this is all gonna be over to. So based on this, when we plug in H equals zero. Now we get two F prime of X over two. So it's just going to give us f prime of X. Um as our final answer and therefore we've proven this.

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