- #1
alba_ei
- 39
- 1
Homework Statement
[tex]
\lim_{x \to - \infty} \frac{3^x-3^{-x}}{3^x+3^{-x}}
[/tex]
Homework Equations
[tex]
\lim_{x \to - \infty} \frac{3^x-3^{-x}}{3^x+3^{-x}} = - 1
[/tex]
The Attempt at a Solution
Im getting trouble when I try to evaluate this limit, altough the answer is -1 idont know how to get to it.
[tex]
\lim_{x \to - \infty} \frac{3^x-3^{-x}}{3^x+3^{-x}}
[/tex]
[tex]
= \lim_{x \to - \infty} \frac{3^{-x}(3^{2x}-1)}{3^{-x}(3^{2x}+1)}
[/tex]
[tex]
= \lim_{x \to - \infty} \frac{3^{2x}-1}{3^{2x}+1}
[/tex]
[tex]
= \lim_{x \to - \infty} \frac{1-\frac{1}{3^{2x}}}{1+\frac{1}{3^{2x}}}
[/tex]
[tex]
= \lim_{x \to - \infty} \frac{1}{1} = 1
[/tex]
I got 1, not -1
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