I dont get if the this calculus and limit question with absolute value...plz help--i choose best answer....--?

Question

im suppose to explain why this limit is true or false and to give an example that disproves it, if it is false.. please help!

lim
x->0 |x| / x = 1

Answer 1

Examine the limit from both the left and the right.

From the left, |x| = -x, and -x/x = -1.
From the right, |x| = x, and x/x = 1.

Since the left <> the right, that limit is false.

Answer 2

FALSE

absolute value of a positive or negative number is always positive but x might be positive or negative; when divided by itself, the number will 1 or -1