# How do you graph y=xlnx?

Dec 14, 2016

See tally-mark like graph and explanation.

#### Explanation:

$x > 0$ to make ln x real.

The x-intercept ( y = 0 ) is 1.

At x= o, y takes the indeterminate form $0 X \left(- \infty\right)$

Yet, the limit is 0. since x approaches 0 at a faster rate than ln x

approaches 0, as $x \to {0}_{+}$.

When $x \in \left(0. 1\right] , y < 0$.

As $x \to \infty , y \to \infty$.

graph{y-x ln x=0 [-2.338, 2.337, -1.168, 1.17]}