\(\lim\limits_{x\rightarrow0}\dfrac{\sqrt{x^2+4}+x-2}{x^2-x}=\lim\limits_{x\rightarrow0}\dfrac{\dfrac{\left(\sqrt{x^2+4}-2\right)\left(\sqrt{x^2+4}+2\right)}{\sqrt{x^2+4}+2}+x}{x\left(x-1\right)}\)
\(=\lim\limits_{x\rightarrow0}\dfrac{\dfrac{x^2}{\sqrt{x^2+4}+2}+x}{x\left(x-1\right)}=\lim\limits_{x\rightarrow0}\dfrac{\dfrac{x}{\sqrt{x^2+4}+2}+1}{x-1}\)
\(=\dfrac{0+1}{-1}=-1\)
tính giới hạn
a) \(\lim\limits_{x\rightarrow4}\dfrac{\sqrt{2x+8}-4}{x-4}\)
b) \(\lim\limits_{x\rightarrow2}\dfrac{x^2-4}{\sqrt{4x+1}-3}\)
c) \(\lim\limits_{x\rightarrow2}\dfrac{x-2}{2-\sqrt{x+2}}\)
11) \(\lim\limits_{x->1}\) \(\dfrac{3_{\sqrt{4x-1}-\sqrt{4x-3}}}{x-1}\)
11) \(\lim\limits_{x->4}\dfrac{4x-1}{x^2-8x+16}\)
12) \(\lim\limits_{x->2}\)\(\dfrac{4-x^2}{x^3-8}\)
13) \(\lim\limits_{x->+\infty}\left(3_{\sqrt{x^3+4x^2}-x}\right)\)
4. Tính giới hạn \(\lim\limits_{x\rightarrow0}\dfrac{\sqrt{x^2+1}-x-1}{2x^2-x}_{ }\)
5. Tính giới hạn:
a) \(\lim\limits_{x\rightarrow2}\dfrac{x-2}{x^2-4}_{ }\)
b) \(\lim\limits_{x\rightarrow3^-}\dfrac{x+3}{x-3}_{ }\)
a) \(\lim\limits_{x\rightarrow1}\dfrac{\sqrt{2x+2}+\sqrt{5x+4}-5}{x-1}_{ }\)
b) \(\lim\limits_{x\rightarrow0}\dfrac{\sqrt{4x+4}+\sqrt{90-6x}-5}{x^2}\)
1) \(\lim\limits_{x\rightarrow4}\dfrac{\sqrt{2x+1}-\sqrt{x+5}}{x-4}\)
2) \(\lim\limits_{x\rightarrow0}\dfrac{\sqrt{1-x}-\sqrt{1+x}}{x}\)
tính giới hạn
a) \(\lim\limits_{x\rightarrow3}\dfrac{\sqrt{2x+10}-4}{3x-9}\)
b) \(\lim\limits_{x\rightarrow7}\dfrac{\sqrt{4x+8}-6}{x^2-9x+14}\)
c) \(\lim\limits_{x\rightarrow5}\dfrac{x^2-8x+15}{2x^2-9x-5}\)
tính giới hạn lim(x→0)\(\dfrac{ }{\dfrac{2\sqrt{2x+1}-\sqrt[3]{x^2+x+8}}{x}}\)
=\(\dfrac{a}{b}\)
tính a-2b=?
Giúp mình với ạ
1) lim\(\dfrac{3x^2+5}{x^3-x+2}\)(x-->+∞)
2) lim\(\dfrac{2x^2\left(3x^2-5\right)^3\left(1-x\right)^5}{3x^{14}+x^2-1}\)(x-->-∞)
3) lim\(\dfrac{3x-\sqrt{2x^2+5}}{x^2-4}\)(x-->+∞)
\(a,\lim\limits_{x\rightarrow0}\dfrac{\sqrt{x+1}-\sqrt{x^2+x+1}}{x^2-2x+1}\)
\(b,\lim\limits_{x\rightarrow7}\dfrac{\sqrt{x-3}-2}{49-x^2}\)
