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Compute the limit (exponents with variable)

  • #1

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

  • #2
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?
 
  • #3
Dick
Science Advisor
Homework Helper
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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'.
 

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