If f(x) = text{Sgn}(text{Sgn}(text{Sgn}(x))), | vedclass

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

Question

(D) The signum function $	ext{Sgn}(x)$ is defined as:$	ext{Sgn}(x) = 1$ if $x > 0$,$	ext{Sgn}(x) = -1$ if $x

Vedclass · Accepted Answer

does not exist

Vedclass · Answer

(D) The signum function $	ext{Sgn}(x)$ is defined as:$	ext{Sgn}(x) = 1$ if $x > 0$,$	ext{Sgn}(x) = -1$ if $x For $x > 0$,$	ext{Sgn}(x) = 1$,so $	ext{Sgn}(	ext{Sgn}(x)) = 	ext{Sgn}(1) = 1$,and $	ext{Sgn}(	ext{Sgn}(	ext{Sgn}(x))) = 	ext{Sgn}(1) = 1$.Thus,$\mathop {\lim }\limits_{x 	o 0^+} f(x) = 1$.For $x Thus,$\mathop {\lim }\limits_{x 	o 0^-} f(x) = -1$.Since the left-hand limit $(-1)$ is not equal to the right-hand limit $(1)$,the limit $\mathop {\lim }\limits_{x 	o 0} f(x)$ does not exist.

If $f(x) = \text{Sgn}(\text{Sgn}(\text{Sgn}(x)))$,then $\mathop {\lim }\limits_{x \to 0} f(x)$ is equal to :-

Similar Questions

Evaluate the given limit: $\mathop {\lim }\limits_{x \to 1} \frac{a x^{2}+b x+c}{c x^{2}+b x+a}$,where $a+b+c \neq 0$.

$\lim _{x \rightarrow-\infty} \frac{3|x|^3-x^2+2|x|-5}{-5|x|^3+3 x^2-2|x|+7} = $

Evaluate the given limit: $\mathop {\lim }\limits_{x \to 3} \frac{x^{4}-81}{2 x^{2}-5 x-3}$

The value of $\lim _{x \rightarrow \infty}\left(\frac{x^{2}-2 x+1}{x^{2}-4 x+2}\right)^{x}$ is

$\mathop {\lim }\limits_{x \to {2^ + }} \frac{{1 - \cos \{ {x^2} + 2x\} }}{{\ln {{(x - 1)}^{(x - 2)}}}}$ is equal to (where $\{.\}$ denotes fractional part function).

Vedclass Test Series

Exam Paper Generator

Online Exam Module