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1

Solved example of limits

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

Multiplying the fraction and term

$\lim_{x\to∞}\left(e^x+\frac{-1}{e^x}\right)^{\left(\frac{1}{x^2}\right)}$
3

The limit of a sum of two functions is equal to the sum of the limits of each function: $\displaystyle\lim_{x\to c}(f(x)\pm g(x))=\lim_{x\to c}(f(x))\pm\lim_{x\to c}(g(x))$

$\left(\lim_{x\to∞}\left(e^x\right)+\lim_{x\to∞}\left(\frac{-1}{e^x}\right)\right)^{\left(\frac{1}{x^2}\right)}$
4

Evaluating the limit when $x$ tends to $∞$

$\left(e^∞+\lim_{x\to∞}\left(\frac{-1}{e^x}\right)\right)^{\left(\frac{1}{x^2}\right)}$
5

Evaluating the limit when $x$ tends to $∞$

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

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