Question

Find the value of ‘a’ for which the function f defined as

f(x)={s sin π/2(x+1),x≤0  ,(tanx-sinx)/x³,x>0

is continuous at x = 0.

Answer 1

f(x) is continuous at x = 0.
=>(L.H.L. of f(x) at x = 0) = (R.H.L. of f(x) at x = 0) = f(0)

Now,

Putting above values in (i) we get, a = 1/2