Simple limit question?

Question

i might be looking to deeply into this, but i can't seem to solve it:

lim x -> 2 of (x + 3)/(x - 2)

i think it does not exist, but not sure. can someone help me? thanks!

Answer 1

you're right. The limit does not exist.

if you just plug in 2, you get 5/0. whenever you get an undefined statement like this, the limit does not exist. In this case there is a vertical asymptote at x = 2.

if you plugged in 2 and got 0/0 which is an indeterminate form, then the limit would exist and you'd have some work to do. This type is the most common.

ps. here are a couple reasons why the girl below me is wrong

1) negative infinity, positive infinity, whatever infinity is never an answer to a limit problem. The answer is always a number or it does not exist.

2) as x approaches 2 from the left, the graph DOES shoot down into negative infinity, but as x approaches 2 from the right, the graph goes to positive infinity. The limit from the left does not equal the limit from the right. Even if they both headed towards positive infinity from both sides, the limit still wouldn't exist. Infinity is never an answer. You can use 'infinity' to describe end behavior, but as far as a final answer to a limit problem, it's not.

Answer 2

There is no answer as x -> 2. If you replace x with 2, you get them sum 5 / 0 ... and you cannot divide by 0.

There is an asymptote on the line x = 2. x can never be 2, therefore the graph cannot cross it.

Answer 3

negative infinity