Tìm giới hạn lim x→+∞ 10x^4.3√x+x+1/x^5+x^4+x+2.

Question

Tìm giới hạn \({\mathop{\lim }\limits_{x\to +\infty }} \frac{10x^{4} .\sqrt[{3}]{x} +x+1}{x^{5} +x^{4} +x+2} .\)

\(A. -\infty . \)

\(B. -1. \)

\(C. 0. \)

\(D. +\infty .\)

Answer 1

Chọn C

Ta có

\({\mathop{\lim }\limits_{x\to +\infty }} \frac{10x^{4} .\sqrt[{3}]{x} +x+1}{x^{5} +x^{4} +x+2} ={\mathop{\lim }\limits_{x\to +\infty }} \frac{x^{5} \left(\frac{10}{\sqrt[{3}]{x^{2} } } +\frac{1}{x^{4} } +\frac{1}{x^{5} } \right)}{x^{5} \left(1+\frac{1}{x} +\frac{1}{x^{4} } +\frac{2}{x^{5} } \right)} ={\mathop{\lim }\limits_{x\to +\infty }} \frac{\frac{10}{\sqrt[{3}]{x^{2} } } +\frac{1}{x^{4} } +\frac{1}{x^{5} } }{1+\frac{1}{x} +\frac{1}{x^{4} } +\frac{2}{x^{5} } } =0\)