10. Show that f (x) = { x² sin(1/x) if x + 0 if x is differentiable, but the derivative is not continuous at x = 0.
10. Show that f (x) = { x² sin(1/x) if x + 0 if x is differentiable, but the derivative is not continuous at x = 0.
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.
Chapter3: The Derivative
Section3.CR: Chapter 3 Review
Problem 59CR
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Question
Show that
f(x) =
x 0 2 sin(1=x) | if if x x 6= 0 = 0 |
is differentiable, but the derivative is not continuous at x = 0
![10. Show that
f (x) = {
x² sin(1/x) if x +0
if x = 0
is differentiable, but the derivative is not continuous at x = 0.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F187d6ce3-f16e-4919-9795-1c801fb3fce4%2F92dec6c4-0c12-4f68-bc82-e4528ded9961%2F75k0ltl_processed.jpeg&w=3840&q=75)
Transcribed Image Text:10. Show that
f (x) = {
x² sin(1/x) if x +0
if x = 0
is differentiable, but the derivative is not continuous at x = 0.
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