How do you evaluate the limit: lim_(x->oo)(e^(-2x)-e^(2x))/(e^(-2x)+e^(2x))?

1 Answer
Sep 15, 2017

-1.

Explanation:

First of all, divide everything in the limit by the highest power, so in this case, e^(2x).
lim_"x->∞"(e^(-4x)-1)/(e^(-4x)+1)
Use the following property:
lim_"x->a"[f(x)/g(x)]=(lim_"x->a"f(x))/(lim_"x->a"g(x)) = (lim_"x->∞"e^(-4x)-1)/(lim_"x->∞"(e^(-4x)+1) = (lim_"x->∞"1/(e^(4x))-1)/(lim_"x->∞"(1/(e^(4x))+1)

Now, to solve the limit. Just by glancing at it, lim_"x->∞"1/(e^(4x)) looks like it is basically 0, so we can write that in.

(0-1)/(0+1) = -1/1 = -1.
And there you go!