The points of discontinuity of $\tan x$ are

Important Questions on Continuity and Differentiability

MEDIUM

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 2>Chapter 5 - Continuity and Differentiability>Target Exercises>Q 9

The set of point(s) of discontinuity of the function $\frac{1}{\log \left|x\right|}$ is

HARD

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 2>Chapter 5 - Continuity and Differentiability>Target Exercises>Q 10

The point(s) of discontinuity of the function $f\left(x\right)=\left\{\begin{array}{cl}\frac{1}{5}\left(2x^2+3\right),& x\le 1\\ 6-5x,& 1<x<3\\ x-3,& x\ge 3\end{array}\right.$ is/are

MEDIUM

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 2>Chapter 5 - Continuity and Differentiability>Target Exercises>Q 11

For the function $f\left(x\right)=\left\{\begin{array}{ll}x-1,& x<0\\ \frac{1}{4},& x=0\\ x^2,& x>0\end{array}\right.,$$\underset{x\to 0^{+}}{\lim }f\left(x\right)$ and $\underset{x\to 0^{-}}{\lim }f\left(x\right)$ are 

HARD

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 2>Chapter 5 - Continuity and Differentiability>Target Exercises>Q 12

If $f$ is a periodic function, then

HARD

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 2>Chapter 5 - Continuity and Differentiability>Target Exercises>Q 13

If $f\left(x\right)=\left\{\begin{array}{cl}\frac{\sin \left(\cos x\right)-\cos x}{{\left(\pi -2x\right)}^2},& x\ne \frac{\pi }{2}\\ k,& x=\frac{\pi }{2}\end{array}\right.$ is continuous at $x=\frac{\pi }{2}$, then $k$ is equal to

MEDIUM

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 2>Chapter 5 - Continuity and Differentiability>Target Exercises>Q 14

Let $f\left(x\right)=\left\{\begin{array}{cl}\frac{x^4-5x^2+4}{\left|\left(x-1\right)\left(x-2\right)\right|},& x\ne 1,2\\ 6,& x=1\\ 12,& x=2\end{array}\right.$. Then, $f\left(x\right)$ is continuous on the set

MEDIUM

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 2>Chapter 5 - Continuity and Differentiability>Target Exercises>Q 16

The function $f\left(x\right)=\left\{\begin{array}{cl}{\left(x+1\right)}^{2-\left(\frac{1}{\left|x\right|}+\frac{1}{x}\right)},& x\ne 0\\ 0,& x=0\end{array}\right.$ is 

HARD

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 2>Chapter 5 - Continuity and Differentiability>Target Exercises>Q 17

If $f\left(x\right)=\left\{\begin{array}{cc}\frac{1-{\sin }^{2}x}{3{\cos }^{2}x},& x<\frac{\pi }{2}\\ a,& x=\frac{\pi }{2}\\ \frac{b\left(1-\sin x\right)}{{\left(\pi -2x\right)}^2},& x>\frac{\pi }{2}\end{array}\right.$. Then, $f\left(x\right)$ is continuous at $x=\frac{\pi }{2}$, if