Question #fbfbb

1 Answer
May 12, 2017

Find the left- and right-sided limit, if they are the same, then the two-sided limit has the same value, otherwise the two-sided limit does not exist. Answer: lim_(x->0)1/x does not exist

Explanation:

Formatted question: Find lim_(x->0)1/x

Since clearly we cannot find the limit by simply substituting, because x=0 is a vertical asymptote, we need to find the limit as x approaches 0 from the left- and right-sided limits:
lim_(x->0^-)1/x=-oo
lim_(x->0^+)1/x=oo

Since left-sided limit does not equal the right-sided limit, therefore, the two-sided limit does not exist:
lim_(x->0)1/x does not exist