Question

limx-> 0 (1/x - 1/|x|)

Answer 1

\[\Large\bf\sf \lim_{x\to0}\frac{1}{x}-\frac{1}{|x|}\]Are we approaching from the left or right of zero?
Or that's not specified?

Answer 2

that's not specified

Answer 3

\[\Large\bf\sf \frac{1}{|x|}\quad=\quad \frac{1}{x},\qquad x>0\]\[\Large\bf\sf \frac{1}{|x|}\quad=-\frac{1}{x},\qquad x< 0\]

So when we're approaching zero from the left side we have,\[\Large\bf\sf \lim_{x\to0^-}\frac{1}{x}-\left(-\frac{1}{x}\right)\]And from the right,\[\Large\bf\sf \lim_{x\to0^+}\frac{1}{x}-\frac{1}{x}\]

For the limit to exist (with neither left nor right specificed),
the limits from the left and right have to agree.

Answer 4

Evaluate both of those limits. Determine whether or not you get the same values.

Answer 5

ok Thank you

Answer 6

welcome c: