Question

Why is this limit 0?

Answer 1

\[\lim_{x \rightarrow \infty}xln(x)\]

Answer 2

WAIT, it's as x->0 sorry!

Answer 3

ln(0) does not exist. So shouldn't this limit not exist?

Answer 4

As x approaches zero. The value of x is approaching zero, but never reaches zero. However, we know that ln(1)=0, so values that are getting closer and closer to zero will be approximated to zero

Answer 5

But if you see the x value in front, anything multiplied by zero is also zero

Answer 6

Okay, thanks