Download the App!
Get 24/7 study help with the Numerade app for iOS and Android! Enter your email for an invite.
Question
Answered step-by-step
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.
Video Answer
Solved by verified expert
This problem has been solved!
Try Numerade free for 7 days
Like
Report
Official textbook answer
Video by Carson Merrill
Numerade Educator
This textbook answer is only visible when subscribed! Please subscribe to view the answer
02:22
Wen Zheng
01:50
Amrita Bhasin
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
Campbell University
Oregon State University
University of Michigan - Ann Arbor
Lectures
04:35
In mathematics, the volume of a solid object is the amount of three-dimensional space enclosed by the boundaries of the object. The volume of a solid of revolution (such as a sphere or cylinder) is calculated by multiplying the area of the base by the height of the solid.
06:14
A review is a form of evaluation, analysis, and judgment of a body of work, such as a book, movie, album, play, software application, video game, or scientific research. Reviews may be used to assess the value of a resource, or to provide a summary of the content of the resource, or to judge the importance of the resource.
01:10
If $f^{\prime}$ is continu…
01:34
(a) Let $f^{\prime}(x)$ be…
01:18
If $ f" $ is continuo…
04:58
Let $f^{\prime \prime}(x)$…
If $f^{\prime \prime}$ is …
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.
View More Answers From This Book
Find Another Textbook
02:09
The diameter of a circle is 20 miles. What is the angle measure of an arc bo…
01:41
PLZ HELP WILL GIVE BRAINLIEST!!! AND 20 POINTS!!!!!!!!!!!Frank opens sev…
01:20
Matt's parents pay him $5.50 for each half hour he babysits his sister,…
01:06
(08.03)A set of equations is given below: Equation C: y = 6x + 9 Equ…
01:22
8TH GRADE MATH PLEASE HALP ME BRAILIEST!!!!(06.01)A scatter plot is made wit…
01:01
Crop yield is the ratio of the number of bushels harvested to the number of …
02:11
Hank bought 5 meters of ribbon for $4. The ribbon costs -$0.008, 0.08, $0.8-…
05:29
A store charges their customers based on the number of items that they buy. …
01:42
the surface area of a cylinder is given by the formula SA = 2πr2 2πrh, whe…
01:39
In a high school of 1250 students, 250 are freshmen and 150 students take Sp…