If f(x)={(ax+1",", x le (pi)/(2)),(sinx+...

If `f(x)={(ax+1",", x le (pi)/(2)),(sinx+b",", x gt (pi)/(2)):}` is continuous, then

a=1,b=0

`a=bpi/2 +1`

`b=a pi/2`

a=b=pi//2`

Text Solution

Verified by Experts

The correct Answer is:

Topper's Solved these Questions

LIMITS AND CONTINUITY
MCGROW HILL PUBLICATION|Exercise Exercise (Numerical Answer)|16 Videos
LIMITS AND CONTINUITY
MCGROW HILL PUBLICATION|Exercise Questions for Previous Years AIEEE/JEE Main Papers|44 Videos
LIMITS AND CONTINUITY
MCGROW HILL PUBLICATION|Exercise Exercise (Level 1 Single Correct Answer)|39 Videos
JEE (MAIN) QUESTIONS WITH SOLUTIONS MATHEMATICS (7 TH JAN-MORNING )
MCGROW HILL PUBLICATION|Exercise QUESTIONS|25 Videos
MATHEMATICAL INDUCTION AND BINOMIAL THEOREM
MCGROW HILL PUBLICATION|Exercise Questions from Previous Years. B-Architecture Entrance Examination Papers|20 Videos

Similar Questions

Explore conceptually related problems

If f(x) = {(ax+1,",",x le (pi)/(2)),(sin x+ b,",",x gt (pi)/(2)):} is continuous at x = (pi)/2 , then

If f(x)=[{:(mx+1,if x le (pi)/(2)),(sinx+n,ifxgt(pi)/(2)):} is continuous at x = (pi)/(2) , then

If f(x)={{:(mx+1,xle(pi)/(2)),(sinx+n,xgt(pi)/(2)):} is continuous at x=(pi)/(2) . Then which one of the following is correct?

If f(x)={(((1-sin^(3)x))/(3cos^(2)x)",",x lt (pi)/(2)),(a",",x=(pi)/(2)),((b(1-sinx))/((pi-2x)^(2))",",x gt (pi)/(2)):} is continuous at x=(pi)/(2) , then the value of ((b)/(a))^(5//3) is

If f:R to R given by f(x)={(2cosx"," , "if", x le -(pi)/(2)),(a sin x+b",","if", -(pi)/(2) lt x lt (pi)/(2)),(1+cos^(2)x",","if",x ge(pi)/(2)):} is a continuous function on R, then (a, b) is equal to

If f(x)={(x+a sqrt(2) sinx"," ,0 lt x lt (pi)/(4)),(2x cotx+b",",(pi)/(4) le x le (pi)/(2)),(a cos 2x-b sinx",", (pi)/(2) lt x le pi):} is continuous at x=(pi)/(4) , then a - b is equal to

The value of a and b such that the function f(x)={(-2sinx"," , -pi le x le -(pi)/(2)),(a sinx+b",", -(pi)/(2) lt x lt (pi)/(2)),(cosx",", (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

If f(x)={{:((1-sqrt2sinx)/(pi-4x)",",ifxne(pi)/(4)),(a",",if x=(pi)/(4)):} in continuous at (pi)/(4) , then a is equal to :

If f (x) = {{:(x + 1 , x le 1), (3 - ax^(2) ,x gt 1):} is continuous at x =1, then the value of a is

MCGROW HILL PUBLICATION-LIMITS AND CONTINUITY-Exercise (Level 2 Single Correct Answer)

The value of lim(x-> -4) (tanpix)/(x+4) + lim(x->oo)(1+1/x^2)^x is
Text Solution
|
The value of lim(x to 0) ("sinx"/x)^("sin x"/"x-sinx") is
Text Solution
|
The value of lim(x->0)((sinx-tanx)^2-(1-cos2x)^4+x^5)/(7(tan^(- 1)x)^7...
Text Solution
|
Let f(x)=x-1 and g(x)=1/x. Then the set of points where gofog is conti...
Text Solution
|
Let f(x)=lim( n to oo) ([x^2]+[(2x)^2]+... + [(nx)^2])/n^3 then the se...
Text Solution
|
If : f(x){:( =1", ... x is rational"),(=0", ...x is irr...
Text Solution
|
Let f(x) be given that f(x)={{:(,x,"if x is rational"),(,1-x,"if x is ...
Text Solution
|
Let f:R to R be any function. Defining g: R to R by g(x)=|f(x)|" for "...
Text Solution
|
Let f be a function defined on R by f(x)=lim(n to oo) (log (3+x)-x^(2n...
Text Solution
|
If f(x)=((x^2+5x+3)/(x^2+x+2))^x then lim(xtooo)f(x) is equal to
Text Solution
|
Let f(x) be defined for all > x0 and be continuous. Let f(x) satisfies...
Text Solution
|
Given the function f(x)=1/(1-x), the numbers of discontinuities of f^...
Text Solution
|
If f(x)=(1+sinx-cosx)/(1-sinx-cosx), x ne 0 . The value of f(0) so tha...
Text Solution
|
If f(x)={(ax+1",", x le (pi)/(2)),(sinx+b",", x gt (pi)/(2)):} is cont...
Text Solution
|
If f(x)={((x^(3)+x^(2)-16x+20)/((x-2)^(2))",",x ne 2),(k",", x =2):} ...
Text Solution
|
f(x) ={{:((2^(x+2)-16)/(4^(x)-16), if x ne 2 ),(k, if x = 2):} ,x = 2.
Text Solution
|
If the function f(x) = (cos^(2)x - sin^(2)x-1)/(sqrt(x^(2)+1)-1), x !=...
Text Solution
|
If a and b are positive integers then
Text Solution
|
Let f(x)=(tan[e^2]x^2-tan[-e^2]x^2)/(sin^2x), x!=0 then the value of f...
Text Solution
|
The value of f(0) so that the function f(x)= (cos a x - cos bx)/x^2 ,...
Text Solution
|