3. (a) (b) By using the limit definition of the derivative, calculate f'(x) if f(x): = 1 X for all x R\{0}. show that the function g(x) = |x3| is differentiable at the point x = 0. Then, determine whether the function g'(x) is continuous at x = 0.

3. (a) (b) By using the limit definition of the derivative, calculate f'(x) if f(x): = 1 X for all x R\{0}. show that the function g(x) = |x3| is differentiable at the point x = 0. Then, determine whether the function g'(x) is continuous at x = 0.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

3.
(a)
(b)
By using the limit definition of the derivative,
calculate f'(x) if f(x):
=
1
X
for all x R\{0}.
show that the function g(x) = |x3| is differentiable at the point x = 0.
Then, determine whether the function g'(x) is continuous at x = 0.

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