A function is f(x) = begin{cases} frac{e^{1/x | vedclass

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

Question

(B) To check the continuity at $x=0$,we evaluate the left-hand limit $(LHL)$ and right-hand limit $(RHL)$.For $LHL$: $\lim_{x 	o 0^-} f(x) = \lim_{h

Vedclass · Accepted Answer

not continuous at $x=0$

Vedclass · Answer

(B) To check the continuity at $x=0$,we evaluate the left-hand limit $(LHL)$ and right-hand limit $(RHL)$.For $LHL$: $\lim_{x 	o 0^-} f(x) = \lim_{h 	o 0} \frac{e^{1/(0-h)}-1}{e^{1/(0-h)}+1} = \lim_{h 	o 0} \frac{e^{-1/h}-1}{e^{-1/h}+1}$. Since $e^{-1/h} 	o 0$ as $h 	o 0^+$,$LHL$ $= \frac{0-1}{0+1} = -1$.For $RHL$: $\lim_{x 	o 0^+} f(x) = \lim_{h 	o 0} \frac{e^{1/h}-1}{e^{1/h}+1} = \lim_{h 	o 0} \frac{1-e^{-1/h}}{1+e^{-1/h}} = \frac{1-0}{1+0} = 1$.Since $LHL$ $
eq$ $RHL$,the limit does not exist at $x=0$.Therefore,the function is not continuous at $x=0$.

$A$ function is $f(x) = \begin{cases} \frac{e^{1/x}-1}{e^{1/x}+1}, & \text{if } x \neq 0 \\ 0, & \text{if } x=0 \end{cases}$

Similar Questions

If $f(x) = \frac{3^{x+3} - 3^{-x} - 2}{\tan x \cdot \log(1+x)}$ for $x \neq 0$, is continuous at $x = 0$, then the value of $f(0)$ is equal to ...

Prove that the function $f(x) = x^{n}$ is continuous at $x = n$,where $n$ is a positive integer.

If the function $f(x) = \begin{cases} k_{1}(x-\pi)^{2}-1, & x \leq \pi \\ k_{2} \cos x, & x>\pi \end{cases}$ is twice differentiable,then the ordered pair $(k_{1}, k_{2})$ is equal to

The number of point / points where the function $f(x) = \frac{1}{x^2 - 5|x| + 6}$ is discontinuous is......

Which of the following functions is not continuous at $x = 0$?

Vedclass Test Series

Exam Paper Generator

Online Exam Module