GATE 2013 MA Calculus

Question

Answer 1

option A is correct.

if We expand f(x), then it is something like,

f(x)= sinx/1 + sin2x/4 + sin3x/9 + sin4x/16 ..........................so on.

apply limit x->0 , all the Numerator turns out to be zero.

so Overall the result is going to be zero.