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Step-by-step Solution

Find the limit $\lim_{x\to∞}\left(e^x-\frac{1}{e^x}\right)^{\left(\frac{1}{x^2}\right)}$

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Answer

$\left(e^∞+\frac{-1}{e^∞}\right)^{\left(\frac{1}{x^2}\right)}$

Step-by-step explanation

Problem to solve:

$\lim_{x\to∞}\left(e^x-\frac{1}{e^x}\right)^{\frac{1}{x^2}}$
1

Multiplying the fraction and term

$\lim_{x\to∞}\left(e^x+\frac{-1}{e^x}\right)^{\left(\frac{1}{x^2}\right)}$

Unlock this step-by-step solution!

Answer

$\left(e^∞+\frac{-1}{e^∞}\right)^{\left(\frac{1}{x^2}\right)}$
$\lim_{x\to∞}\left(e^x-\frac{1}{e^x}\right)^{\frac{1}{x^2}}$

Main topic:

Limits

Related formulas:

1. See formulas

Time to solve it:

~ 0.05 seconds

Related topics:

Limits

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