Question

How do you find the limit of `((t^2) + 2)/(t-4)` as t approaches 4?

Answer 1

Limit does not exist

Explanation:

start by plugging in 4

`(4^2 + 2)/(4-4)` so we see that this goes to `oo` at `t = 4`

the numerator is always positive

....whereas the denominator is negative for `t = 4 - delta` and positive for `t = 4 + delta`, where `0 < delta " << " 1` so we have a two-sided limit

`lim_(t to 4^-) ((t^2) + 2)/(t-4) = -oo`

`lim_(t to 4^+) ((t^2) + 2)/(t-4) = oo`

Therefore limit does not exist