Find mathop {lim }limits_{x to 0} f(x) where | vedclass

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

Question

(D) To find $\mathop {\lim }\limits_{x 	o 0} f(x)$,we evaluate the left-hand limit $(LHL)$ and the right-hand limit $(RHL)$.$LHL$: $\mathop {\lim }\l

Vedclass · Accepted Answer

Does not exist

Vedclass · Answer

(D) To find $\mathop {\lim }\limits_{x 	o 0} f(x)$,we evaluate the left-hand limit $(LHL)$ and the right-hand limit $(RHL)$.$LHL$: $\mathop {\lim }\limits_{x 	o 0^-} f(x) = \mathop {\lim }\limits_{x 	o 0^-} \frac{x}{|x|}$.Since $x $RHL$: $\mathop {\lim }\limits_{x 	o 0^+} f(x) = \mathop {\lim }\limits_{x 	o 0^+} \frac{x}{|x|}$.Since $x > 0$,$|x| = x$,so $\mathop {\lim }\limits_{x 	o 0^+} \frac{x}{x} = \mathop {\lim }\limits_{x 	o 0^+} (1) = 1$.Since $\mathop {\lim }\limits_{x 	o 0^-} f(x) 
eq \mathop {\lim }\limits_{x 	o 0^+} f(x)$,the limit $\mathop {\lim }\limits_{x 	o 0} f(x)$ does not exist.

Find $\mathop {\lim }\limits_{x \to 0} f(x)$ where $f(x) = \begin{cases} \frac{x}{|x|}, & x \neq 0 \\ 0, & x=0 \end{cases}$

Similar Questions

If $[x]$ is the greatest integer function,then $\lim _{x \rightarrow 2^{+}}\left(\frac{[x]^3}{3}-\left[\frac{x}{3}\right]^3\right)=$

$\lim _{x \rightarrow 3 / 2} \frac{\left(4 x^2-6 x\right)\left(4 x^2+6 x+9\right)}{\sqrt[3]{2 x}-\sqrt[3]{3}}=$

The value of the limit of $\frac{x^3 - 8}{x^2 - 4}$ as $x \to 2$ is

If $l, m$ $(l < m)$ are roots of $ax^2 + bx + c = 0$,then $\lim_{x \rightarrow \alpha} \frac{|ax^2 + bx + c|}{ax^2 + bx + c} = $

If $\lim _{n \rightarrow \infty} x^n \log _e x=0$,then $\log _x 12=$

Vedclass Test Series

Exam Paper Generator

Online Exam Module