Question #fbfbb

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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

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