Which of the following functions is different | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(D) Let $f(x) = \sin(|x|) - |x|$. We check the differentiability at $x = 0$ by calculating the Left Hand Derivative $(LHD)$ and Right Hand Derivative

Vedclass · Accepted Answer

$\sin (|x|) - |x|$

Vedclass · Answer

(D) Let $f(x) = \sin(|x|) - |x|$. We check the differentiability at $x = 0$ by calculating the Left Hand Derivative $(LHD)$ and Right Hand Derivative $(RHD)$.For $x For $x > 0$,$|x| = x$,so $f(x) = \sin x - x$. The derivative is $f'(x) = \cos x - 1$. Thus,$RHD = \lim_{x 	o 0^+} (\cos x - 1) = \cos(0) - 1 = 1 - 1 = 0$.Since $LHD = RHD = 0$,the function $\sin(|x|) - |x|$ is differentiable at $x = 0$.For the other options,$\cos(|x|)$ is differentiable at $x=0$ but $|x|$ is not,so their sum or difference is not differentiable at $x=0$. Similarly,$\sin(|x|) + |x|$ has $LHD = -2$ and $RHD = 2$,so it is not differentiable.

Which of the following functions is differentiable at $x = 0$?

Similar Questions

Let $f(x) = |x|$. Then which of the following is true?

Let $f(x)=|1-2 x|$, then

$f(x)= \begin{cases} 2a-x & \text{in } -a < x < a \\ 3x-2a & \text{in } a \leq x \end{cases}$
Then,which of the following is true?

If $f(x) = \begin{cases} ax^2 + b; & x \le 0 \\ x^2; & x > 0 \end{cases}$ possesses a derivative at $x = 0$,then:

$\text{The domain of the derivative of the function } f(x) = \begin{cases} \tan^{-1} x, & \text{if } |x| \le 1 \\ \frac{1}{2}(|x|-1), & \text{if } |x| > 1 \end{cases} \text{ is given by:}$

Vedclass Test Series

Exam Paper Generator

Online Exam Module