Here is the question:

Prove that:

lim [x -> 0+] sqrt(x) e^sin(pi / x) = 0

(for clarification, it's a right-hand limit)

What's throwing me off here is the exponent of e, sin(pi / x) since that itself is undefined, and I'm unsure how that affects the question.

My friend has said that it's equal to zero because it is all values greater than zero, limited at zero.

How could I go about proving the initial limit statement?