Question

How do you find the limit of `(x^2+5)/(x^2-4)` as x approaches `-oo`?

Answer 1

I would say it tends to `1`

Explanation:

We can try manipulating our function and write it as:
`lim_(x->-oo)=(cancel(x^2)(1+5/x^2))/(cancel(x^2)(1-4/x^2))=`
as `x->-oo` the two remaining fractions tends to zero so we get:
`lim_(x->-oo)=(1+5/x^2)/(1-4/x^2)=(1+0)/(1-0)=1`

We can see this tendency graphically plotting our function:

graph{(x^2+5)/(x^2-4) [-10, 10, -5, 5]}