Question

find the limit. lim (x-5)/((x^2)-25) x-> 5+
i got 1/10 when i computed the limit but when i graph it, i don't see how it's 1/10...

Answer 1

This is a factoring problem. (x-5)/[(x-5)(x+5)]

AWAY from x = 5, your function is EXACTLY 1/(x+5).
AT x = 5, it doesn't exist.

Answer 2

That should be x=-5 where it does not exist. Vertical asymptote.

Answer 3

It has an asymptote at x = -5 and also fails to exist, there.

It also doesn't exist at x = 5. This is sometimes called "a hole".

Answer 4

Ah yes if you look at the original function and question. My bad :).