for what value of a is the following equation true? lim ((x+a)/(x-a))^x = e x->inf
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Take the natural log of both sides, so that you wind up with: Now use L'Hôpital's rule to find .
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?
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.
im not seeing how this is a piece of cake?
Originally Posted by pnfuller im not seeing how this is a piece of cake? LEARN this: Yours can be rewritten an .
Sorry, bad choice of words. What is ?
the limit as a^2/x^2 approaches infinity equals 0? is that what you mean?
Yes, so what does that tell you about the limit at the end of post #4?
that the limit as x approaches infinity is 1/1 and it equals 1 but what does a equal?
Reread that equation carefully. You were told
Okay, since the limit is 1, you simply have: Now solve for .
so a = 1/2
Originally Posted by pnfuller that the limit as x approaches infinity is 1/1 and it equals 1 but what does a equal? This whole thread is totally frustrating for me. Please look at reply #5. The answer is . WHY?
why is it frustrating for you?
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