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

May 18, 2018

Does not exist.

#### Explanation:

As $x$ approaches $0$, $\sin \left(\frac{1}{x}\right)$ takes on values $- 1$ and $1$, infinitely many times.

The value cannot be approaching a single limiting number and ${e}^{x} \sin \left(\frac{1}{x}\right)$ is indefined in the interval $\left(- 1 , 1\right)$

Here is a graph to help understand this more

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