If f(x)={:{((sin2x)/(sqrt(1-cos2x))", fo...

If `f(x)={:{((sin2x)/(sqrt(1-cos2x))", for " 0 lt x le pi/2),((cos x)/(pi-2x)", for "pi/2 lt x le pi):}`

f is continuous on its domain except `x=pi/2`

f is continuous on its domain

f is discontinuous on its domain

f is continuous on its domain except `x=0`

Text Solution

Verified by Experts

The correct Answer is:

Topper's Solved these Questions

BINOMIAL DISTRIBUTION
NIKITA PUBLICATION|Exercise MCQS|77 Videos
DEFINITE INTEGRAL
NIKITA PUBLICATION|Exercise MULTIPLE CHOICE QUESTIONS|243 Videos

Similar Questions

Explore conceptually related problems

If f(x)={:{((sin 2x)/(sqrt(1-cos 2x))", for " 0 lt x lt pi/2),((cos x)/(pi-2x)", for " pi/2 lt x lt pi):} , then

Diseuss the continuity of the function : {:(f(x)=(sin 2x)/(sqrt(1-cos2x)),",for"0ltx le(pi)/(2)),(=(cosx)/(pi-2x),",for" (pi)/(2)ltx ltpi):}}at x=(pi)/(2)*

If f(x)={:{(x sin x", for " 0 lt x le pi/2),(pi/2 sin (pi+x)", for " pi/2 lt x lt pi):} , then

Let f(x)={{:(x^2+4x "," -3 le x le 0),(-sin x ","0 lt x le pi//2 ),(-cos x -1 "," pi//2 lt x le pi):} which one of the following is not true ?

If : f(x) {:(=x.sin x ", ... " 0 lt x le pi/2),(=pi/2 sin (pi+x)", ... "pi/2ltxltpi):} , then

Let f(x)={(sinx+cosx",",0 lt x lt (pi)/(2)),(a",",x=pi//2),(tan^(2)x+"cosec"x",",pi//2 lt x lt pi):} Then its odd extension is

Let f(x) = {{:(sgn(x)+x",",-oo lt x lt 0),(-1+sin x",",0 le x le pi//2),(cos x",",pi//2 le x lt oo):} , then number of points, where f(x) is not differentiable, is/are

Let f(x) = {{:(-2 sin x,"for",-pi le x le - (pi)/(2)),(a sin x + b,"for",-(pi)/(2) lt x lt (pi)/(2)),(cos x,"for",(pi)/(2) le x le pi):} . If f is continuous on [-pi, pi) , then find the values of a and b.

The value of a and b such that the function f(x) {:{(-2 sin x", "-pile x le -pi/2 ),(a sin x+b " ," -pi/2 lt x lt pi/2 ),(cos x", " pi/2 le x le pi ):} is continuous in [ - pi , pi ] are

If the function f(x)={(x+a^(2)sqrt(2)sinx",", 0 le x lt (pi)/(4)),(x cot x+b",",(pi)/(4) le x lt (pi)/(2)),(b sin 2x-a cos 2x",", (pi)/(2) le x le pi):} is continuous in the interval [0,pi] then the values of (a, b) are

NIKITA PUBLICATION-CONTINUITY-MULTIPLE CHOICE QUESTIONS

If f(x)={:{((sinx)/(x)", for " x lt 0),(x+1", for " x ge 0):}, then
Text Solution
|
If f(x)={((2x+5)/(x+1)", for " 0 le x lt 2),(4x-5", for " 2 le x le 4)...
Text Solution
|
If f(x)={:{((sin2x)/(sqrt(1-cos2x))", for " 0 lt x le pi/2),((cos x)/(...
Text Solution
|
If f(x)={:{(x", for " 0 le x lt 1),(2", for " x=1),(x+1", for " 1 lt x...
Text Solution
|
If f(x)=(x^(3)+3x+5)/(x^(3)-3x+2) in [0, 5], then f is
Text Solution
|
If f(x)=(x+1)/((x-2)(x-5)), then in [4, 6]
Text Solution
|
If f(x)=(x+1)/((x-2)(x-5)), then in [0, 1]
Text Solution
|
If f(x)={:{(x", for " x ge 0),(x^(2)", for " x lt 0):}, then f is
Text Solution
|
If f(x)={:{(x^(2)-4", for " 0 le x le 2),(2x+3", for " 2 lt x le 4),(x...
Text Solution
|
If f(x)={((1)/(x+1)", for " 2 le x le 4),((x+1)/(x-3)", for " 4 lt x l...
Text Solution
|
If f(x)={:{(3", if " 0 le x le 1),(4", if " 1 lt x lt 3),(5", if " 3 l...
Text Solution
|
If f(x)={:{(-2", for " x le -1),(2x", for " -1 lt x le 1),(2", for " x...
Text Solution
|
f(x)={(|x|+3",","if", x le -3),(-2x",", "if", -3 lt x lt 3),(6x+2",","...
Text Solution
|
If f(x)={(2x", for " x lt 0),(2x+1", for " x ge 0):} , then
Text Solution
|
Function f(x)={(x-1",",x lt 2),(2x-3",", x ge 2):} is a continuous fun...
Text Solution
|
If f(x)=(x^(3)-8)/(x^(2)+x-20), then
Text Solution
|
If f(x)={:{((x^(2)-3x+2)/(x-3)", for " 0 le x lt 4),((x^(2)-1)/(x-2)",...
Text Solution
|
If the function f(x)=k +x, "For" x lt1 =4x+3, "For" x ge1 is co...
Text Solution
|
If f(x) is continuous at x=0, where f(x)={:{(x^(2)+1", for " x ge 0),...
Text Solution
|
If f(x) is continuous at x=0, where f(x)={:{(k(x^(2)-2)", for " x le ...
Text Solution
|