Question

What is `lim_(x->0) e^x*sin(1/x)`?

Answer 1

Does not exist.

Explanation:

As `x` approaches `0`, `sin(1/x)` takes on values `-1` and `1`, infinitely many times.

The value cannot be approaching a single limiting number and `e^xsin(1/x)` is indefined in the interval `(-1,1)`

Here is a graph to help understand this more

graph{e^xsin(1/x) [-4.164, 4.604, -1.91, 2.473]}