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Question Number 138997 by bramlexs22 last updated on 21/Apr/21

$$\underset{x\to 1}{\lim }\frac{\sqrt[3]{7+{\mathrm{x}}^3}-\sqrt{3+{\mathrm{x}}^2}}{\mathrm{x}-1}=?$$

Answered by EDWIN88 last updated on 21/Apr/21

$$\underset{x\to 1}{\lim }\frac{{\mathrm{x}}^2{(7+{\mathrm{x}}^3)}^{-\frac{2}{3}}-\mathrm{x}{(3+{\mathrm{x}}^2)}^{-\frac{1}{2}}}{1}$$$$=\frac{8^{-\frac{2}{3}}-4^{-\frac{1}{2}}}{1}=\frac{1}{4}-\frac{1}{2}=-\frac{1}{4}$$

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