If f(x) = sin(a+1)x + 2sin x / x, x < 0; = 2, x = 0; = √(1+bx) / x, x > 0 is continuous at x = 0, then find the values of a and b.

At x=0 function is continuous, limx→0+f(x) = limx→0-f(x) = f(0)
RHL:= limx→0+f(x) = limx→0f(0+h) = limx→0√(1+bh)/h × √(1+bh)+1/√(1+bh)+1 = limx→0(1+bh)/h(√(1+bh)+1) = limx→0bh/(√(1+bh)+1) = b/2
f(0) = 2
LHL:= limx→0-f(x) = limh→0f(0-h) = limh→0sin((a+1)(0-h)) + sin(0-h)/(0-h) = limh→0sin(-(a+1)h) + sin(-h)/-h = limh→0-(a+1)h/h + (-h)/h = -(a+1) -1 = -(a+2) = 2 ⇒ a = -3
b/2 = 2 ⇒ b = 4