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$\lim_{x \to 0} \frac{x\left(e^{\sqrt{1+x^2+x^4}-1)/x} - 1\right)}{\sqrt{1+x^2+x^4} - 1}$ is equal to:
(1) is equal to $\sqrt{e}$
(2) is equal to $1$
(3) is equal to $0$
(4) does not exist
Let $\frac{\sqrt{1+x^2+x^4}-1}{x} = t$. When $x \to 0$, $t \to 0$. Then $L = \lim_{t\to 0}\frac{e^t - 1}{t} = 1$.
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