Horizontal asymptote for e function

Hello,

The function is

I managed to get to the first horizontal asymptote by using lhospital's rule after I got to this:

But then the sign of infinity which I insert doesn't matter because y will always be 1, and I know that there's another asymptote in y=-1.

How do I get to the other asymptote? Have I done anything wrong?

Re: Horizontal asymptote for e function

I would rewrite the function as:

a) For the asymptote as

b) For the asymptote as

Re: Horizontal asymptote for e function

How did you get to that function?

Re: Horizontal asymptote for e function

If you're asking about a) then MarkFL2 is dividing both the numerator and denominator with . Doing this wont change the value of the fraction and hence is a good way to get a fraction were we easy can calculate the limit.

Re: Horizontal asymptote for e function

Yes, for:

a)

b)

Re: Horizontal asymptote for e function

So I always have to get to a certain equation of the same function in order to get its limits?

How do I know when to keep trying to look for a way I can get the limit and when to let it go because it has no horizontal asymptote?

Re: Horizontal asymptote for e function

Sometimes it is helpful to rewrite a function to more easily determine its limit, particularly limits at plus/minus infinity. When there is no horizontal asymptote, you should be able to show that the limit does not exist.