Question

Find the limit as x approaches infinity:
limits as x approaches infinity of (2^X-3^x)/(3^x+4^x). And L'hopital's rule cannot be used.

Answer 1

\[(2^x-3^x)/(3^x+4^x) \]

Answer 2

Limit of sums = Sum of limits.

The limit of the quotient = Quotient of limits

The limit of a Constant = The Constant

tell me what you get up to this point.

Answer 3

what exactly do you want me to do here?

Answer 4

I want you to apply the rules, and separate and simplify the limits as much as you can.

Answer 5

Actually I got a lecture soon, so buy

Answer 6

bye

Answer 7

Factor 3^x out of the numerator as well as the denominator and cancel them. Then take the limits of the numerator and the denominator.

Answer 8

Okay, I'll try that.

Answer 9

I got: \[\frac{ ((2/3)^x-1) }{ 1+(4/3)^x}\]

Answer 10

Did I do that correctly? The final answer should be 0.

Answer 11

Now take the limit of the numerator separately and the limit of the denominator separately.

Answer 12

Doing so would give me -1/1, which isn't the right answer..

Answer 13

oh wait

Answer 14

Sorry I got the answer. Thank you!

Answer 15

2/3 is less than 1. When it is raised to x it will be an exponential decay function that attains zero when x approaches infinity.
4/3 is greater than 1. When it is raised to x it will be an exponential growth function that becomes unbounded when x approaches infinity.