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Question Number 113598 by bobhans last updated on 14/Sep/20

Answered by bemath last updated on 14/Sep/20

$$letmesolve$$$$\underset{x\to \mathrm{\infty }}{\lim }\sqrt[3]{27x^3(1+\frac{1}{3x^2})}-\sqrt[4]{64x^4(1-\frac{1}{8x^3})}=$$$$\underset{x\to \mathrm{\infty }}{\lim 3}x\sqrt[3]{1+\frac{1}{3x^2}}-2x\sqrt[4]{1-\frac{1}{8x^3}}=$$$$\underset{x\to \mathrm{\infty }}{\lim }3x(1+\frac{1}{9x^2})-2x(1-\frac{1}{32x^3})=\mathrm{\infty }$$$$$$

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