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Calculate $\displaystyle \lim_{x \to 0} \frac{x^2-\sin^2{x}}{\tan(3x^4)}$ How does one calculate this limit? Is it valid to say, since $\sin^2{x}$ is approximated by $x^2$ as $x \to 0$ , we have:   $\displaystyle \lim_{x \to 0} \frac{x^2-\sin^2{x}}{\tan(3x^4)}$  $=\lim_{x \to 0} \frac{x^2-x^2}{\tan(3x^4)} =0$

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