Home
Class 12
MATHS
f(x)={x+sqrt2asinx,0ltxltpi/4 and 2xcotx...

`f(x)={x+sqrt2asinx,0ltxltpi/4 and 2xcotx+b , pi/4lexltpi/2 and acosx-bsinx , pi/2lexltpi `. Determine the value of a and b If function is continuous for interval `[0,pi]`

Text Solution

Verified by Experts

Here, value of `f(x)` is changing at `pi/2` and `pi/4`.
So, `f(x)` to be continuous,
`f((pi/4)^-) = f((pi/4)^+)`
`=>pi/4+sqrt2 a*1/sqrt2 = 2*pi/4(1)+b`
`=>pi/4 +a = pi/2+b`
`=>a-b = pi/4->(1)`
Also, `f(x)` to be continuous,
`f((pi/2)^-) = f((pi/2)^+)`
...
Promotional Banner

Similar Questions

Explore conceptually related problems

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

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

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

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

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

the function f(x)=(6/5)^((tan6x)/(tan5x)) if x is 0 to pi/2 and f(x)=b+2 if x=pi/2 and f(x)=(1+|cosx|)^{(a*|tanx|)/b} if x is pi/2 to pi Determine the values of a&b. if f is continuous at x=pi/2

Find the values of a and b such that the function f (x) defined by f(x)={{:(x+asqrt(2)sinx,0lexlt(pi)/(4)),(2xcotx+b,(pi)/(4)lexle(pi)/(2)),(acos2x-bsinx,(pi)/(2)ltxlepi):} is continuous for all values of x in 0lexlepi .

The function f(x)={x+a sqrt(2)sin x,0<=x<=(pi)/(4) and 2x cot x+b,(pi)/(4)<=x<=(pi)/(2) and a cos2x-b sin x,(pi)/(2), is continuous for 0<=x<=pi ,then value of a,b 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