for what value of a is the following equation true?

lim ((x+a)/(x-a))^x = e

x->inf

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- Nov 6th 2012, 10:12 AMpnfullerlimits / equations?
for what value of a is the following equation true?

lim ((x+a)/(x-a))^x = e

x->inf - Nov 6th 2012, 10:57 AMMarkFLRe: limits / equations?
Take the natural log of both sides, so that you wind up with:

Now use L'Hôpital's rule to find . - Nov 6th 2012, 12:03 PMpnfullerRe: limits / equations?
after applying L'Hôpital's rule i got the limit as x approaches infinity ((x-a)(-2a))/(-x^-2) = 1

and now what do i do from there? - Nov 6th 2012, 12:13 PMMarkFLRe: limits / equations?
You have differentiated the numerator incorrectly. You want:

Now, putting this together with the derivative of the denominator, we have:

which we can write as:

From here, it is a piece of cake. - Nov 6th 2012, 12:20 PMpnfullerRe: limits / equations?
im not seeing how this is a piece of cake?

- Nov 6th 2012, 12:36 PMPlatoRe: limits / equations?
- Nov 6th 2012, 12:37 PMMarkFLRe: limits / equations?
Sorry, bad choice of words. :)

What is ? - Nov 6th 2012, 12:42 PMpnfullerRe: limits / equations?
the limit as a^2/x^2 approaches infinity equals 0? is that what you mean?

- Nov 6th 2012, 01:09 PMMarkFLRe: limits / equations?
Yes, so what does that tell you about the limit at the end of post #4?

- Nov 6th 2012, 03:06 PMpnfullerRe: limits / equations?
that the limit as x approaches infinity is 1/1 and it equals 1 but what does a equal?

- Nov 6th 2012, 03:10 PMProve ItRe: limits / equations?
Reread that equation carefully. You were told

- Nov 6th 2012, 03:11 PMMarkFLRe: limits / equations?
Okay, since the limit is 1, you simply have:

Now solve for . - Nov 6th 2012, 03:19 PMpnfullerRe: limits / equations?
so a = 1/2

- Nov 6th 2012, 03:21 PMPlatoRe: limits / equations?
- Nov 6th 2012, 03:26 PMpnfullerRe: limits / equations?
why is it frustrating for you?