3 Show that the function f(x) =2x — |x| is continuous but not differentiable at x=0 4 - Maths - Continuity and Differentiability

Question

3 Show that the function f(x) =2x — |x| is continuous but not
differentiable at x=0
4 Find the value of k, for Which the function
f ( x )   = 1 + k x - 1 - k x x ,   i f   - 1 ≤ x
< 0 2 x + 1 x - 1 ,   i f   0 ≤ x < 1 is
continuous at x=O

Richa Kumari · Accepted Answer

Please find this answer
<img src=
"https://s3mn%20mnimgs%20com/img/shared/content_ck_images/ck_5aad69739e890%20jpeg">

3. Show that the function f(x) =2x — |x| is continuous but not differentiable at x=0. 4. Find the value of k, for Which the function f ( x ) = 1 + k x - 1 - k x x , i f - 1 ≤ x < 0 2 x + 1 x - 1 , i f 0 ≤ x < 1 is continuous at x=O.

3. Show that the function f(x) =2x — |x| is continuous but not differentiable at x=0.
4. Find the value of k, for Which the function
$f (x) = \{\begin{cases} \frac{\sqrt{1 + k x} - \sqrt{1 - k x}}{x}, i f - 1 \leq x < 0 \\ \frac{2 x + 1}{x - 1}, i f 0 \leq x < 1 \end{cases}$ is continuous at x=O.