If function f(x) = {(a+bsqrt(2)sinx, 0 l...

If function `f(x) = {(a+bsqrt(2)sinx, 0 le xlt pi/4),(cotx-1, pi/4lexle(3pi)/4),(b sin 2x+3, (3pi)/4lt xle pi):}` is continuous `AA x in [x,pi]`, then a+b is equal to

Text Solution

Verified by Experts

The correct Answer is:

Topper's Solved these Questions

CONTINUITY AND DIFFERENTIABILITY
CENGAGE|Exercise Solved Examples And Exercises|108 Videos
CONIC SECTIONS
CENGAGE|Exercise Solved Examples And Exercises|91 Videos
COORDINATE SYSTEM
CENGAGE|Exercise Multiple Correct Answers Type|2 Videos

Similar Questions

Explore conceptually related problems

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

Find the values of a and b so that the function f(x)={{:(x+asqrt2 sin x", "0 le x le pi//4),(2x cot x + b", "pi//4 le x le pi//2),(a cot 2x - b sin x", "pi//2 lt x le pi):} is continuous for 0 le x le pi .

The values of a and b so that the function f(x) = {{:(x + a sqrt(2) sin x",",0 le x lt pi//4),(2 x cot x + b",",pi//4 le x le pi//2),(a cos 2 x - b sin x",",pi//2 lt x le pi):} is continuous for x in [0, pi] , are

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

f(x)= {:{(x+asqrt2 sin x ,, 0 le x lt pi/4),( 2x cot x +b , , pi/4 le x le pi/2), (a cos 2 x - b sin x , , pi/2 lt x le pi):} continuous function AA x in [ 0,pi] " then " 5(a/b)^(2) equals ....

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

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

CENGAGE-CONTINUITY AND DIFFERENTIABILITY-Question Bank

Let f(x) = {(sqrt(x^(2)-1), x le sqrt10),((sqrt(10x)-7), sqrt10lt xlt...
Text Solution
|
Let f(x) = sqrt(x^(2)+px+1)/(x^(2)-p). If f(x) is discontinuous at exa...
Text Solution
|
Number of points of non-derivability of the function f(x) = root (3)((...
Text Solution
|
If f(x) = {(lim(x rarr oo)(6^(t)+10^(t))^(1/t), x = 0),(x^(2)+4x+C, x ...
Text Solution
|
Number of point(s) in [1,2] where f(x) = (-2)^([x^(3)]) is non-differe...
Text Solution
|
Consider the function f(x) = {(a^(2)+e^(x), -oo lt x lt 0),(x+2, 0le x...
Text Solution
|
Let f(x) = [(sqrt(1+sin^(2)(x^(2))-cos^(3)(x^(2)))/(x^(3)tanx), if x n...
Text Solution
|
Let f(x) = {(cos(x^(3)), -ooltxlt0),(sin(x^(3))-|x^(3)-1|, 0lexltoo):}...
Text Solution
|
The sum of all values of x for which the function f(x) = sqrt(|x^(2)-5...
Text Solution
|
Let f(x) = [(-1, -3 le x lt 0),(x-1, 0le xle 3):} and g(x) = f(|x|)+|f...
Text Solution
|
Let f(x) be a differentiable function satisfying f((x+2y)/3)= (f(x)+2f...
Text Solution
|
Let f(x) = {((sin alphax^(2))/x^(2), x ne 0),(3/4+1/(4alpha), x = 0):}...
Text Solution
|
Let f(x) = {(a tan^(-1)(1/(x-4)), 0 lexlt4),(pi/2, x= 4),(btan^(-1)(2/...
Text Solution
|
Let f(x) = {((1+ax)^(1/x), x lt 0),((root(3)(x+c)-1)/(sqrt(x+1)-1), x ...
Text Solution
|
The number of points in (-5,5) where f(x)=[x](x^(3)-x)^(2)) is non-dif...
Text Solution
|
If f(x) = cos (x (cos)1/x) and g(x) = (In(sec^(2)x))/(x sin x) are bot...
Text Solution
|
Consider , f(x) = {(|(x-x^(3) 1 2),(0 2 3x^(4)),(x^(2) 4x x^(3)-3x^(5)...
Text Solution
|
Number of points where f(x)= max {2-|x|, min {x^(2)-1}} is not differe...
Text Solution
|
If function f(x) = {(a+bsqrt(2)sinx, 0 le xlt pi/4),(cotx-1, pi/4lexle...
Text Solution
|
If f(x) = {((sin^(-1)x-xcos^(-1)x)/x, x gt 0),(ax+b, xle 0):} is conti...
Text Solution
|