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
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
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