Yes, there should be a theorem in your book that says that if and , then .

There should also be theorems that say that, under the same hypotheses,

.

.

and, provided g(x) is not 0 in some neighborhood of a,

.

There is another limit theorem that is not emphasised nearly enough:

If f(x)= g(x) for all xexcepta, the

So that if, for example for all x and for all xexceptx= 1 and g(1)= 1000, then .