- #1

binbagsss

- 1,265

- 11

## Homework Statement

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Trying to understand this limit:

where ##r>0##

## Homework Equations

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I think it's best to proceed by writing this as:

## N=1 \pm \frac{\sqrt{Ae^{2rt}}}{\sqrt{1-Ae^{2rt}}} ##

## The Attempt at a Solution

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since ##r>0 ## the exponential term ##\to ## ##\infty## and then since ##A<0## I get two results for ## lim_{t \to \infty} Ae^{2rt} ## depending on ## |A| ##.

a) If ##|A| < 1 ## it goes to zero.

if b) ## |A| \geq 1 ## it goes to ##-\infty##

and where the magnitude of A is not specified in the question.

If it was however for case a) the limit is of an determinate form: ##1 \pm \frac{0}{1} = 1 ##

however for b) i get ## 1 \pm \frac{\sqrt{-\infty}}{\sqrt{1+\infty}}## , and I can't see L'Hopitals rule being much use here due to the square root and exponential terms.

Many thanks in advance.