Question

find the limit:
lim as x approaches -infinity, (e^x-e^-x)/(e^x+e^-x)

Answer 1

are you factoring something there myininaya ?
:)

Answer 2

Divide top and bottom by e^-x and you have
\[(e^{2x}-1)/(e^{2x}+1)\]

Now the limit as x -> -inf of the numerator and denominator is finite and non-zero. Namely, -1/1 hence the limit is -1.

Answer 3

By the way, dividing by e^-x is the same as multiplying by e^x, which is perhaps slightly more intuitive.

Answer 4

why do you divide by e^-x? I thought the numerator and denominator were set as they are and cant be manipulated?

Answer 5

i got -1

Answer 6

Of course we can manipulate fractions. For example look at 1/2. Multiply top and bottom by 2 and you get 2/4. This is in principle identical to what we just did.