If f(x)={:{(x sin x", for " 0 lt x le pi...

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

f(x) is discontinous at `x = pi/2`

f(x) is continous at `x = pi/2`

f(x) is continous at `x = 0`

none of these

Text Solution

Verified by Experts

The correct Answer is:

Topper's Solved these Questions

CONTINUITY
TARGET PUBLICATION|Exercise Competitive Thinking|63 Videos
CONTINUITY
TARGET PUBLICATION|Exercise Evaluation Test|10 Videos
CONTINUITY
TARGET PUBLICATION|Exercise Evaluation Test|10 Videos
BINOMIAL DISTRIBUTION
TARGET PUBLICATION|Exercise EVALUTION TEST|12 Videos
DEFINITE INTEGRALS
TARGET PUBLICATION|Exercise EVALUATIO TEST|30 Videos

Similar Questions

Explore conceptually related problems

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

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

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):}

If : f(x) {:(=1", ... "0 ltx le (3pi)/4), (= 2 .sin ((2x)/9) ", ..." (3pi)/4lt x lt pi):} then :

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 f(x) = {(1, ",", "when" 0 lt x le (3pi)/4),(2(sin) 2/9x, ",", "when" (3pi)/4 lt x lt pi):} , then

If f(x) is continuous in (-oo, 6) , where f(x)={: {(1+sin ((pi x)/(2))", for " - oo lt x le 1),(ax+b", for " 1 lt x lt 3),(6 tan ((pi x)/(12))", for " 3 le x lt 6):} , then

TARGET PUBLICATION-CONTINUITY-Critical Thinking

The function f(x) = (4-x^(2))/(4x-x^(3)) is
Text Solution
|
If f(x) ={(4-3x,",",0 lt x le 2),(2x-6,",",2 lt x le 3),(x+5,",",3 lt ...
Text Solution
|
If f(x)={:{(x sin x", for " 0 lt x le pi/2),(pi/2 sin (pi+x)", for " p...
Text Solution
|
If f(y)={(((e^(2y)-1)*siny)/(y^(2)),", for "y ne 0),(4,", for "y=0):}...
Text Solution
|
For the function f(x)={((sin^(2)ax)/(x^(2))",","where " x ne 0),(1",",...
Text Solution
|
The points of discontinuity of tan x are
Text Solution
|
If f(x)={:{((sin 2x)/(sqrt(1-cos 2x))", for " 0 lt x lt pi/2),((cos x)...
Text Solution
|
If {:(f(x),=(x cos x - 3tan x)/(x^(2)+2sinx),",",x != 0),(,=1, ",",x =...
Text Solution
|
If f(x) ={((5^(x)-e^(x))/(sin 2x),",",x != 0),(1/2(log 5+1),",",x = 0)...
Text Solution
|
f(x)={((5^(cosx)-1)/((pi)/(2)-x)",", x ne (pi)/(2)), (log 5"," , x =(p...
Text Solution
|
If f(x) {:( =((2^(x)-1)^(2))/(sin x.log(1+x))", if " x != 0 ),(= ...
Text Solution
|
If f(x) = (tan(pi/4-x))/(cot2x), x != pi/4, is continuous in (0, pi/2)...
Text Solution
|
If f(x)={((sqrt(1+px)-sqrt(1-px))/(x) ",", -1 le x lt 0),((2x+1)/(x-2...
Text Solution
|
The function f(x) = (x^(2)-4)/(sin x-2) is
Text Solution
|
If f(x) is continuous on [0, 8] , where f(x)={:{(x^(2)+ax+6", for " 0...
Text Solution
|
If f(x) is continuous in [-2,2], where f(x) = {((sinax)/(x)-2,",","f...
Text Solution
|
The value of a and b such that the function defined by f(x) = {(7,",...
Text Solution
|
If f(x)=(e^(x)+e^(-x)-2)/(x sin x), for x in [(-pi)/(2), (pi)/(2)]-{0}...
Text Solution
|
Discuss the continuity of f(x)={(x^4-5x^2+4)/(|(x-1)(x-2)),x!=1,2 6,x=...
Text Solution
|
The values of a and b so that the function f(x) = {{:(x + a sqrt(2) si...
Text Solution
|