Đáp án:a)\(\frac{5}{3}\)
b)0
c)0
Giải thích các bước giải:
a)\(\lim_{x\rightarrow -\infty}\frac{\sqrt{x^{2}+3x}+4x}{\sqrt{4x^{2}+1}-x+2}\)
=\(\lim_{x\rightarrow -\infty}\frac{\sqrt{1+\frac{1}{x}}+4}{\sqrt{4+\frac{1}{x}}-1+\frac{2}{x}}\)
=\(\frac{5}{3}\)
b)\(\lim_{x\rightarrow +\infty}(\sqrt{x+2}-\sqrt{x-1})\)
=\(\lim_{x\rightarrow +\infty}(\sqrt{\frac{1}{x}+\frac{2}{x^{2}}}-\sqrt{\frac{1}{x}-\frac{1}{x^{2}}})\)
=0
c)\(\lim_{x\rightarrow +\infty}x(\sqrt{x^{2}+7}-x)\)
=\(\lim_{x\rightarrow +\infty}1(\sqrt{1+\frac{7}{x^{2}}}-1)\)=0
