Continuity of a Function

IMPORTANT

Continuity of a Function: Overview

This topic covers concepts such as Continuity of a Function, Continuity of a Function at a Point, Discontinuity of a Function, Removable and Non-Removable Discontinuities, Ways to Remove a Removable Discontinuity, Infinite Discontinuity, etc.

Important Questions on Continuity of a Function

MEDIUM
IMPORTANT

Find the value of p and q for which the function

fx=sinp+1xsinxx,   x<0q                      x=0x+x2-xx32,       x>0

is continuous for all x in R,

HARD
IMPORTANT

Let gx  be a polynomial of degree one and fx  be a continuous and differentiable function defined by fx=gx,x01+x2+x1x,x>0. If f'1=f'-1, then

HARD
IMPORTANT

If  f x = [ x + x + x sin x for x 0 0 for x = 0 where x denotes the fractional part function, then:

EASY
IMPORTANT

Choose the correct statement on the continuity of the function f given by  fx=x,if x0x2,if x<0at x=0

MEDIUM
IMPORTANT

Choose the correct comment explaining the continuity of the function f defined by   f( x )={ x+2, ifx<1 0, ifx=1 x2, ifx>1 at x=1.

EASY
IMPORTANT

 

If   f(x)={ x 2 25 x5 , whenx5 k, whenx=5   is continuous at   x=5,   then

HARD
IMPORTANT

An example of a function which is continuous but not differentiable is

HARD
IMPORTANT

Consider the function fx=x112x. The value of f2 so that f is continuous at x=2 is -

EASY
IMPORTANT

Function fx=cos1x has oscillatory discontinuity at point x=0.

EASY
IMPORTANT

Function fx=sin1x has oscillatory discontinuity at point x=0.

EASY
IMPORTANT

Define the oscillatory discontinuity with one example.

EASY
IMPORTANT

This is the graph of a function hx.

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Find the x-value at which hx has an isolated point discontinuity.

EASY
IMPORTANT

This is the graph of a function fx. Dashed lines represent asymptotes.

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Select the x-value at which fx has an isolated point discontinuity.

EASY
IMPORTANT

This is the graph of a function fx. Dashed lines represent asymptotes.

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Select the x-value at which fx has a missing point discontinuity.

MEDIUM
IMPORTANT

Let f:RR be defined as

fx=e3xex-e2x+1x2,     if x>0         a,                if x=01cos(2x)x2,             if x<0.

The value of a for which f is continuous at 0 is

HARD
IMPORTANT

If fx=72x-9x-8x+12-1+cosx, x0k2loge2.loge3, x=0 in the interval (0,2π) is continuous, then k is equal to

HARD
IMPORTANT

Let Fx=x-3,x<1x-2+a,x1and Gx=2-x,x<2sgnx-b,x2, where sgnx denotes signum function of x. If Hx=Fx+Gx is continuous for all value of xR, then the value of a and b respectively is 

HARD
IMPORTANT

Number of points of which fx=2+3sinx is discontinuous, where x0,2π are θ1,θ2,θ3,....,θn. Find r=1nθr, where . denotes GIF.

MEDIUM
IMPORTANT

Let gx=1-x;x+2;4-x;0x11<x<22x4, then the numbers of points where ggx is discontinuous is

EASY
IMPORTANT

The number of points of discontinuity of the function f( x )=x[ x ] in the interval ( 0,7 )  are