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`.

Find the values of a and b so that the function `f(x)={{:(x+asqrt2 sin

1.	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`.
Answer» Correct Answer - `a=pi/6, b = (-pi)/12` Since, f(x) is continuous for ` 0 le x le pi` `:." " RHL("at" x = pi/4)= LHL ("at" x = pi/4)` ` rArr" " ( 2* pi/4 cot. Pi/4 + b) = (pi/4 + asqrt2 * sin. Pi/4) ` `rArr" " pi/2 + b = pi/4 + a rArr a - b = pi/4` .....(i) Also, RHL ` ("at" x = pi/2) = LHL ("at" x = pi/2)` ` rArr (a cot (2pi)/2 - b sin. pi/2) = ( 2* pi/2* cot. pi/2 + b) ` `rArr" " -a-b=b` `rArr" " a+ 2b = 0` ....(ii) On solving Eqs. (i) and (ii) , we get ` a = pi/6 and b =- pi/12 `