Let f(x) = begin{cases} frac{tan^2 {x}}{x^2 - | vedclass

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

Question

(D) For $x 	o 0^+$,$[x] = 0$ and $\{x\} = x$. Thus,$\lim_{x 	o 0^+} f(x) = \lim_{x 	o 0^+} \frac{	an^2 x}{x^2 - 0^2} = \lim_{x 	o 0^+} \left( \fr

Vedclass · Accepted Answer

Both $(A)$ and $(C)$

Vedclass · Answer

(D) For $x 	o 0^+$,$[x] = 0$ and $\{x\} = x$. Thus,$\lim_{x 	o 0^+} f(x) = \lim_{x 	o 0^+} \frac{	an^2 x}{x^2 - 0^2} = \lim_{x 	o 0^+} \left( \frac{	an x}{x} ight)^2 = 1^2 = 1$.For $x 	o 0^-$,let $x = -h$ where $h > 0$. Then $[x] = -1$ and $\{x\} = x - [x] = -h - (-1) = 1 - h$.$\lim_{x 	o 0^-} f(x) = \lim_{h 	o 0^+} \sqrt{(1-h) \cot(1-h)} = \sqrt{1 \cdot \cot(1)} = \sqrt{\cot 1}$.Now,$\left( \lim_{x 	o 0^-} f(x) ight)^2 = (\sqrt{\cot 1})^2 = \cot 1$.Therefore,$\cot^{-1} \left( \lim_{x 	o 0^-} f(x) ight)^2 = \cot^{-1}(\cot 1) = 1$.Thus,both $(A)$ and $(C)$ are correct.

Let $f(x) = \begin{cases} \frac{\tan^2 \{x\}}{x^2 - [x]^2} & \text{for } x > 0 \\ 1 & \text{for } x = 0 \\ \sqrt{\{x\} \cot \{x\}} & \text{for } x < 0 \end{cases}$ where $[x]$ is the greatest integer function and $\{x\}$ is the fractional part function of $x$,then:

Similar Questions

If $f(x) = \begin{cases} x e^{-\left( \frac{1}{|x|} + \frac{1}{x} \right)}, & x \ne 0 \\ 0, & x = 0 \end{cases}$,then $f(x)$ is

If $f(x)$ is continuous on its domain $[-2,2]$,where $f(x) = \begin{cases} \frac{\sin ax}{x} + 3, & -2 \leq x < 0 \\ 2x + 7, & 0 \leq x \leq 1 \\ \sqrt{x^2+8} - b, & 1 < x \leq 2 \end{cases}$ then the value of $2a + 3b$ is

Define $f: R \rightarrow R$ by $f(x) = \begin{cases} (x-a) \frac{e^{\frac{1}{x-a}}-1}{e^{\frac{1}{x-a}}+1}, & x \neq a \\ 0, & x=a \end{cases}$. Then which one of the following is true?

If the function $f(x)=\begin{cases} \frac{1-\cos x}{x^{2}}, & \text{for } x \neq 0 \\ k, & \text{for } x=0 \end{cases}$ is continuous at $x=0$,then the value of $k$ is

Let $f(x) = \begin{cases} x+1, & -1 \leq x \leq 0 \\ -x, & 0 < x \leq 1 \end{cases}$. Which of the following statements is true?

Vedclass Test Series

Exam Paper Generator

Online Exam Module