# Compute the limit (exponents with variable)

## Homework Statement

Compute the limits of the following sequence (show your work):

3n+17n+3
4n5n-2

(sorry if it looks funny ... the top line is divided by the bottom line)

## The Attempt at a Solution

I was thinking that I should get the exponents the same and add/subtract the exponents, but I don't remember how to, or if this is even possible.

## Answers and Replies

I think I figured out a bit more. I have learned that I can split up the limit, so it will look like:
(lim3n+1)(lim7n+3) ÷ (lim4n)(lim5n-2)

and each of these individual limits equals +∞.

So I have +∞ ÷ +∞. Does this still equal infinity, 0, or does not exist?

Dick
Science Advisor
Homework Helper
I think I figured out a bit more. I have learned that I can split up the limit, so it will look like:
(lim3n+1)(lim7n+3) ÷ (lim4n)(lim5n-2)

and each of these individual limits equals +∞.

So I have +∞ ÷ +∞. Does this still equal infinity, 0, or does not exist?

Try this. 2^n/3^n=(2/3)^n. What's the limit of that? How about 3^n/2^n? There's a reason why infinity/infinity is called 'indeterminant'.