Find the value of `' a^(prime)` for which the function `f` defined by `f(x)={asinpi/2(x+1),\ \ \ xlt=0(tanx-sinx)/(x^3),\ \ \ x >0` is continuous at `x=0` .

Explanation

`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)`



`lim _{x -> 0^{-}} f(x)=lim _{x -> 0^{+}} f(x)=f(0) ldots(i)`



Now,



`lim _{x -> 0^{-}} f(x)= lim _{x -> 0} a sin frac{pi}{2}(x+1) `


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