Question

Decide if the functions in parts 2-3 are differentiable at $x = 0$. Try zooming in with graphing technology, or calculating the derivative $f'(0)$ from the definition. 2. $f(x) = (x + |x|)^2 + 1$ 3. $f(x) = \begin{cases} x^2 \sin(\frac{1}{x}) & \text{for } x \neq 0\\ 0 & \text{for } x = 0 \end{cases}$

          Decide if the functions in parts 2-3 are differentiable at $x = 0$. Try zooming in with graphing technology, or calculating the derivative $f'(0)$ from the definition.
2. $f(x) = (x + |x|)^2 + 1$
3. $f(x) = \begin{cases} x^2 \sin(\frac{1}{x}) & \text{for } x \neq 0\\ 0 & \text{for } x = 0 \end{cases}$

Decide if the functions in parts 2-3 are differentiable at x = 0. Try zooming in with graphing technology, or calculating the derivative f'(0) from the definition.
2. f(x) = (x + |x|)^2 + 1
3. f(x) = x^2 sin((1)/(x)) for x ≠ 0
0 for x = 0

Added by Jose Miguel S.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Mengchun Cai

09/07/2023

Step 1

Step 1: For function 2, f(x) = (x + |x|)^2 + 1, we need to determine if it is differentiable at x = 0. Show more…

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Decide if the functions in parts 2-3 are differentiable at x=0. Try zooming in with graphing technology, or calculating the derivative f^(')(0) from the definition. 2. f(x)=(x+|x|)^(2)+1 3. f(x)={(x^(2)sin((1)/(x)) for x!=0),(0 for x=0):} Decide if the functions in parts 2-3 are differentiable at x = 0. Try zooming in with graphing technology,or calculating the derivative f'(0) from the definition. 2.fx=x+|x12+1 3.f(x)={x2sin() forx+0 0 forx=o