\(=\lim\limits_{x\rightarrow2}\frac{\sqrt{x+7}-3+\sqrt{3x+10}-4}{x-2}=\lim\limits_{x\rightarrow2}\frac{\frac{x-2}{\sqrt{x+7}+3}+\frac{3\left(x-2\right)}{\sqrt{3x+10}+4}}{x-2}\)
\(=\lim\limits_{x\rightarrow2}\left(\frac{1}{\sqrt{x+7}+3}+\frac{3}{\sqrt{3x+10}+4}\right)=\frac{13}{24}\)
Tính: \(\lim\limits_{x\rightarrow1}\frac{\sqrt{3x-2}+\sqrt[3]{3x+5}-\frac{7}{4}x-\frac{5}{4}}{x^2-2x+1}\)
Tính các giới hạn
a) \(\lim\limits_{x\rightarrow+\infty}\dfrac{x+\sqrt{x^2+x-10}}{2x+3}\)
b) \(\lim\limits_{x\rightarrow+\infty}\dfrac{3x^2+\sqrt{x^2+x-10}}{\sqrt{x^3+x^2-3x-x^2+3}}\)
7)Tính giới hạn:
\(a)\lim\limits_{x\rightarrow+\infty}x\left(\sqrt{x^2+2x}-2\sqrt{x^2+x}+x\right)\)
\(b)\lim\limits_{x\rightarrow+\infty}\left(\sqrt[3]{x^3+3x^2}-\sqrt{x^2-2x}\right)\)
Cho \(\lim\limits_{x\rightarrow5}\dfrac{f\left(x\right)-2}{x-5}=5\). Tính \(\lim\limits_{x\rightarrow5}\dfrac{\sqrt{3f\left(x\right)+10}+\sqrt{f^3\left(x\right)+1}-7}{x^2-25}\)
\(\lim\limits_{x\rightarrow4}\frac{2x-\sqrt{3x+1}}{x^2-1}\)
\(\lim\limits_{x\rightarrow8}\frac{\sqrt[3]{x}-\sqrt{x-4}}{x-8}\)
\(\lim\limits_{x\to 1}\) \(\dfrac{\sqrt[3]{x+7}-\sqrt{x+3}}{x^2-3x+2}\)
Giải hộ mình câu này với
Tìm giới hạn:
a, \(\lim\limits_{x\rightarrow1}\dfrac{\sqrt[3]{x+7}-\sqrt{5-x^2}}{x-1}\)
b, \(\lim\limits_{x\rightarrow5}\dfrac{x-5}{\sqrt{x}-\sqrt{5}}\)
Tìm giới hạn:
a, \(\lim\limits_{x\rightarrow+\infty}\dfrac{x-2}{3-\sqrt{x^2+7}}\)
b, \(\lim\limits_{x\rightarrow-\infty}\dfrac{\sqrt{x^2-x}-\sqrt{4x^2+1}}{2x+3}\)
\(\lim\limits_{x\rightarrow0}\left(\frac{1}{x}+\frac{1}{x^2}\right)\)
\(\lim\limits_{x\rightarrow+\infty}\frac{\sqrt{\left(-x\right)^2+2}}{x-1}\)
\(\lim\limits_{x\rightarrow-\infty}\frac{|x|+\sqrt{x^2+x}}{x+10}\)