If f(x) = begin{cases} frac{1}{x} sin(x^2), & | vedclass

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

Question

(C) To check the continuity of $f(x)$ at $x = 0$,we evaluate the limit as $x 	o 0$.Given $f(x) = \frac{\sin(x^2)}{x}$ for $x 
e 0$.We can rewrite th

Vedclass · Accepted Answer

$f(x)$ is continuous at $x = 0$

Vedclass · Answer

(C) To check the continuity of $f(x)$ at $x = 0$,we evaluate the limit as $x 	o 0$.Given $f(x) = \frac{\sin(x^2)}{x}$ for $x 
e 0$.We can rewrite this as $f(x) = x \cdot \frac{\sin(x^2)}{x^2}$.Now,$\lim_{x 	o 0} f(x) = \lim_{x 	o 0} \left( x \cdot \frac{\sin(x^2)}{x^2} ight)$.Since $\lim_{x 	o 0} \frac{\sin(x^2)}{x^2} = 1$ and $\lim_{x 	o 0} x = 0$,we have $\lim_{x 	o 0} f(x) = 0 \cdot 1 = 0$.Since $\lim_{x 	o 0} f(x) = f(0) = 0$,the function $f(x)$ is continuous at $x = 0$.

If $f(x) = \begin{cases} \frac{1}{x} \sin(x^2), & x \ne 0 \\ 0, & x = 0 \end{cases}$,then

Similar Questions

If $f(x) = \begin{cases} \frac{\sin 5x \tan kx}{x^2} & , x \neq 0 \\ 1 & , x = 0 \end{cases}$ is continuous at $x = 0$,then the value of $k$ is . . . . . . . $(\because k \neq 0)$

If $f(x) = \begin{cases} \frac{3 \sin(\pi x)}{5x} & x \neq 0 \\ 2K & x = 0 \end{cases}$ is continuous at $x = 0$,then the value of $K$ is:

For $x > 0$,let $h(x) = \begin{cases} \frac{1}{q} & \text{if } x = \frac{p}{q} \text{ (where } p, q \in \mathbb{N} \text{ are relatively prime)} \\ 0 & \text{if } x \text{ is irrational} \end{cases}$. Which of the following statements does not hold true?

Let the function $f$ be defined by the equation $f(x) = \begin{cases} 3x & \text{if } 0 \le x \le 1 \\ 5 - 3x & \text{if } 1 < x \le 2 \end{cases}$,then:

Let $f(x) = \begin{cases} |x|, & -\infty < x < 2 \\ |2x-4|, & 2 \leq x \leq 20 \end{cases}$. If $x=a$ is a point where $f(x)$ is continuous but not differentiable and $x=b$ is a point where $f(x)$ is not differentiable $(a \neq b)$,then $a+b=$

Vedclass Test Series

Exam Paper Generator

Online Exam Module