Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
Let f(x) = x² sin(1/x) for x = 0 and f(0) = 0. (a) Use the definition to show f is differentiable at x = 0 and f'(0) = 0. (b) Show f' is not continuous at x = 0.

Let f(x) = x² sin(1/x) for x = 0 and f(0) = 0. (a) Use the definition to show f is differentiable at x = 0 and f'(0) = 0. (b) Show f' is not continuous at x = 0.

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter6: Applications Of The Derivative
Section6.3: Implicit Differentiation
Problem 5E
See similar textbooks
icon
Related questions
Question
Q1 Let f(x) = x² sin(1/x) for x 0 and f(0) = 0. (a) Use the definition to show f is differentiable at x = 0 and f'(0) = 0. (b) Show f' is not continuous at x = 0.
Transcribed Image Text:Q1 Let f(x) = x² sin(1/x) for x 0 and f(0) = 0. (a) Use the definition to show f is differentiable at x = 0 and f'(0) = 0. (b) Show f' is not continuous at x = 0.
Expert Solution
steps

Step by step

Solved in 3 steps with 3 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer