Multiplying and Dividing Limits Examples

If

, and ,

what is

?

The limit of the product is the product of the limits. 

. 

as long as all limits involved exist, this "limit of a product is the product of the limits'' also works even when the product involves several factors.

Assume that  exists, , and .

What is ?

Since all limits involved exist,

.

Assume that  exists, , and .

What is ?

Since exists, so does . Then we can say

.

Assume that  exists and .

What is ?

Since all the limits involved exist, we can pull this apart. First we split the limit across the sum in the numerator, then we'll worry about products.

Now we'll evaluate all the limits we know:

Now we have an equation to solve for .

.