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Question

$\mathop {\lim }\limits_{x \to \infty }(x+1)\sqrt{\frac{x}{2x^{4}+x^{2}+1}}$

score 1 · Answer 1

$= \mathop {\lim }\limits_{x \to +\infty } \sqrt{\frac{x.(x+1)^2}{2x^4+x^2+1}}$

$= \mathop {\lim }\limits_{x \to +\infty } \sqrt{\frac{x^3+2x^2+x}{2x^4+x^2+1}}$

$= \mathop {\lim }\limits_{x \to +\infty } \sqrt{\frac{\frac{1}{x}+\frac{2}{x^2}+\frac{1}{x^3}}{2+\frac{1}{x^2}+\frac{1}{x^4}}}$

$= \sqrt{\frac{0}{2}}=0$

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