Let `f(x)=(lim)_(hvec0)(("sin"(x+h))^(1n(x+h))-(sinx)^(1nx))/hdot` Then `f(pi/2)` equal to 0 (b) equal to 1 In `pi/2` (d) non-existent

Explanation

`"Let "g(x)=(sin x)^(log_(e^(x)))`
`therefore" "f(x)=underset(hrarr0)lim(g(x+h)-g(x))/(h)=g'(x)`
`therefore" "f(x)=g'(x)=(d)/(dx)(e^(log, x. log_(e) sin x))`
`(sin x)^(log_(e)x)((1)/(x)cdotlog_(e) sin x + log_(e) x.(1)/(sin x)cdot cos x)`
`therefore" "f(pi//2)=0`