Home
Class 12
MATHS
If f(x)={{:((2cosx-sin2x)/((pi-2x)^(2))"...

If `f(x)={{:((2cosx-sin2x)/((pi-2x)^(2))",",xle(pi)/(2)),((e^(-cosx)-1)/(8x-4pi)",",xgt(pi)/(2)):}` then which of the following holds?

A

h is continuous at `x = pi//2`

B

h has an irremovable discontinuity at `x = pi//2`

C

h has a removable discontinuity at `x = pi//2`

D

`f((pi^(+))/(2))=g((pi^(-))/(2))`

Text Solution

Verified by Experts

The correct Answer is:
A, C, D
Promotional Banner

Topper's Solved these Questions

  • CONTINUITY AND DIFFERENTIABILITY

    ARIHANT MATHS ENGLISH|Exercise Exercise For Session 4|7 Videos
  • CONTINUITY AND DIFFERENTIABILITY

    ARIHANT MATHS ENGLISH|Exercise Exercise For Session 5|3 Videos
  • CONTINUITY AND DIFFERENTIABILITY

    ARIHANT MATHS ENGLISH|Exercise Exercise For Session 2|4 Videos
  • COMPLEX NUMBERS

    ARIHANT MATHS ENGLISH|Exercise Complex Number Exercise 8|2 Videos
  • COORDINATE SYSTEM AND COORDINATES

    ARIHANT MATHS ENGLISH|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|7 Videos

Similar Questions

Explore conceptually related problems

If f(x)={(2cos x -sin2x)/((pi-2x)^2),xlt=pi/2(e^(-cotx)-1)/(8x-4pi),x >pi/2 , then which of the following holds? (a) f is continuous at x=pi//2 (b) f has an irremovable discontinuity at x=pi//2 (c) f has a removable discontinuity at x=pi//2 (d)None of these

Let f(x)={:{(x^(2)+4x",",-3lexle0),(-sinx",",0ltxle(pi)/(2)),(-cosx-1",",(pi)/(2)ltxlepi):} then

Consider f(x)={{:(cosx,0lexlt(pi)/(2)),(((pi)/(2)-x)^(2),(pi)/(2)lexltpi):} such that f is periodic with period pi . Then which of the following is not true?

Let f(x)={((1+cosx)/((pi-x)^(2)).(sin^(2)x)/(ln(1+pi^(2)-2pix+x^(2))),x ne pi),(lambda, x=pi):}

If f(x)={{:(mx+1",",xle(pi)/(2)),(sinx+n",",xge (pi)/(2)):} is continuous at x=(pi)/(2) , then

If f(x)=(2-3cosx)/(sinx) , then f'((pi)/(4)) is equal to

If f(x)=sin^(2)x+sin^(2)(x+(2pi)/(3))+sin^(2)(x+(4pi)/(3)) then :

If f(x)={((sin(cosx)-cosx)/((pi-2x)^2) ,, x!=pi/2),(k ,, x=pi/2):} is continuous at x=pi/2, then k is equal to

If f(x)={sin^(-1)(sinx),xgt0 (pi)/(2),x=0,then cos^(-1)(cosx),xlt0

If f(x)={sin^(-1)(sinx),xgt0 (pi)/(2),x=0,then cos^(-1)(cosx),xlt0