Question

Evaluate the limit: As x-> 0, lim x/|x|.

Answer 1

\[\lim_{x \rightarrow 0^-}\frac x{|x|}=-1\]\[\lim_{x \rightarrow 0^+}\frac x{|x|}=1\]

Answer 2

What if it just approaches 0, and not from the left or the right?

Answer 3

if the right-hand limit is different than the left-hand limit, the limit does not exist

Answer 4

So, for \[\lim_{x \rightarrow 0} x/|x| \] the limit DNE?

Answer 5

yep

Answer 6

Okay! Now, I see why...thanks!!