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

1 Answer
Aug 25, 2016

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