Question

Question #fbfbb

Answer 1

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