If [x] is the greatest integer function and f | vedclass

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

Question

(D) To check the continuity at $x = 0$: $1$. $f(0) = 1$. $2$. Left-hand limit: $\lim_{x 	o 0^-} f(x) = \lim_{x 	o 0^-} (2[x] - \frac{x}{|x|}) = 2(-1

Vedclass · Accepted Answer

right continuous at $x = 1$

Vedclass · Answer

(D) To check the continuity at $x = 0$: $1$. $f(0) = 1$. $2$. Left-hand limit: $\lim_{x 	o 0^-} f(x) = \lim_{x 	o 0^-} (2[x] - \frac{x}{|x|}) = 2(-1) - (-1) = -2 + 1 = -1$. $3$. Right-hand limit: $\lim_{x 	o 0^+} f(x) = \lim_{x 	o 0^+} (2[x] - \frac{x}{|x|}) = 2(0) - (1) = -1$. Since $\lim_{x 	o 0} f(x) = -1 
eq f(0)$, $f$ is discontinuous at $x = 0$. To check the continuity at $x = 1$: $1$. $f(1) = 2[1] - \frac{1}{|1|} = 2(1) - 1 = 1$. $2$. Left-hand limit: $\lim_{x 	o 1^-} f(x) = \lim_{x 	o 1^-} (2[x] - \frac{x}{|x|}) = 2(0) - 1 = -1$. $3$. Right-hand limit: $\lim_{x 	o 1^+} f(x) = \lim_{x 	o 1^+} (2[x] - \frac{x}{|x|}) = 2(1) - 1 = 1$. Since $\lim_{x 	o 1^+} f(x) = f(1)$, the function is right continuous at $x = 1$.

If $[x]$ is the greatest integer function and $f(x) = \begin{cases} 2[x] - \frac{x}{|x|}, & x \neq 0 \\ 1, & x = 0 \end{cases}$ is a real-valued function, then $f$ is

Similar Questions

For $a, b > 0$,let $f(x) = \begin{cases} \frac{\tan((a+1)x) + b \tan x}{x}, & x < 0 \\ \frac{\sqrt{ax + b^2x^2} - \sqrt{ax}}{b \sqrt{a} x \sqrt{x}}, & x > 0 \end{cases}$ be a continuous function at $x = 0$. Then $\frac{b}{a}$ is equal to

If $f(x) = \begin{cases} x - 1, & x < 0 \\ \frac{1}{4}, & x = 0 \\ x^2, & x > 0 \end{cases}$,then

Which of the following statements is true for the graph of the function $f(x) = \log x$?

Let $[x]$ denote the greatest integer less than or equal to $x$. If $f(x) = [x \sin \pi x]$,then $f(x)$ is

Let $f(x) = \begin{cases} -2 \sin x, & \text{if } x \leq -\frac{\pi}{2} \\ A \sin x + B, & \text{if } -\frac{\pi}{2} < x < \frac{\pi}{2} \\ \cos x, & \text{if } x \geq \frac{\pi}{2} \end{cases}$. For what values of $A$ and $B$ is $f$ continuous?

Vedclass Test Series

Exam Paper Generator

Online Exam Module