Question

`f(x) = (x + 1)/sqrt(x^2 + 4)` Find `lim_(x->+oo) f(x)` and `lim_(x->-oo) f(x)`?

Answer 1

When `x` becomes very big positively (`x->+oo`) your function becomes basically equal to `x/x~=1`.
For example:
`x=1000000`
`f(1000000)=1000000/sqrt((1000000)^2)=1`
When `x` becomes very big negatively you have a big negative number in the numerator and a positive one (it was squared) in the denominator giving -1.
For example:
`x=-1000000`
`f(-1000000)=(-1000000)/sqrt((-1000000)^2)=-1`