Compute lim t→2(5t − 2 + (t^2/t − 1)).

Answer 1

If I understand your typing you want

Lim (5t - 2 + t^2/(t-1)) as t ---> 2

The first thing I do is to sub the approach value into the expression.
This gives us (10 - 2 + 4/1) = 12

So that's it!

If you sub in the approach value, there are 3 possiblities.

a) you get a real number, like in our case. That is your answer. You are done
b) you get c/0, c not equal to zero. This is undefined. So the limit is undefined or infinity.
c) you get 0/0. In that case you have some work ahead of you. In most cases the expression will factor. Furthermore if the approach value is x ---> k making the mess 0/0, then x-k has to turn up as a factor somehow. So at least you know what you are looking for.

Good luck on the rest of the limit problems, if you have any.