Question

Find the limit: lim((x+2)/(x-3))^x as x approaches to positive infinity. Find the limit: lim((x+2)/(x-3))^x as x approaches to positive infinity. @Mathematics

Answer 1

e^5

Answer 2

\[\lim_{x \rightarrow \infty}({x+2\over x-3})^x=\infty\]is all I see. How did you get your answer moneybird?

Answer 3

moneybird can you write down the process ?

Answer 4

yes please

Answer 5

moneybird is correct

Answer 6

can you write down the process Zarkon? because i want to know how.

Answer 7

can you use \[\lim_{x\to\infty}\left(1+\frac{y}{x}\right)^x=e^y\]
?

Answer 8

why do i use that form?

Answer 9

if you know the above then you can use it to find the answer to your problem...

otherwise you can use

\[\left({x+2\over x-3}\right)^x=\exp\left(x\ln\left({x+2\over x-3}\right)\right)\]

\[=\exp\left(\frac{\ln\left({x+2\over x-3}\right)}{1/x}\right)\]

now use L'Hospital's rule

Answer 10

I am stuck with using the rule. Could you tell me how to solve?

Answer 11

write

\[\ln\left({x+2\over x-3}\right)=\ln(x+2)-\ln(x-3)\]

in the above function then

use L'Hospital's rule.

Answer 12

oh okay.