Question

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1. lim ( x đến +--∞) (x³ +3x²+2)

2. lim (x đến -∞) (\(\sqrt{4x^2-x+5}\))

3. lim ( x đến +- ∞) (\(\sqrt{x^2-2x-1}-\sqrt{x^2-7x+3}\))

Answer 1

1.

\(\lim\limits_{x\to +\infty}(x^3+3x^2+2)=+\infty\)

2. 

\(\lim\limits_{x\to -\infty}\sqrt{4x^2-x+5}=\lim\limits_{x\to -\infty}-x.\sqrt{4+\frac{1}{x}+\frac{5}{x^2}}=+\infty\) do $-x\to +\infty$ và $\lim\limits_{x\to -\infty}\sqrt{4+\frac{1}{x}+\frac{5}{x^2}}=4>0$

 

Answer 2

3.

\(\lim\limits_{x\to +\infty}(\sqrt{x^2-2x-1}-\sqrt{x^2-7x+3})=\lim\limits_{x\to +\infty}\frac{x^2-2x-1-(x^2-7x+3)}{\sqrt{x^2-2x-1}+\sqrt{x^2-7x+3}}\)

\(=\lim\limits_{x\to +\infty}\frac{5x-4}{\sqrt{x^2-2x-1}+\sqrt{x^2-7x+3}}=\lim\limits_{x\to +\infty}\frac{5-\frac{4}{x}}{\sqrt{1-\frac{2}{x}-\frac{1}{x^2}}+\sqrt{1-\frac{7}{x}+\frac{3}{x^2}}}\)

\(=\frac{5}{1+1}=\frac{5}{2}\)