Question

What is the limit as x approaches 0 of `e^x sin(x)`?

Answer 1

The first thing you should always try with a limit problem is entering `x` into the function. So let's do that:
`lim_{x to 0}e^xsin(x) = e^0sin(0) = 1*0 = 0`

Et voilà! You have your answer.
Hope this helped.