Lời giải:
\(\lim\limits_{x\to 0}\frac{\sqrt{4+x}(\sqrt[3]{8+3x}-2)+2(\sqrt{4+x}-2)}{x(x+1)}=\lim\limits_{x\to 0}\frac{\sqrt{4+x}.\frac{3x}{\sqrt[3]{(8+3x)^2}+2\sqrt[3]{8+3x}+4}+2.\frac{x}{\sqrt{4+x}+2}}{x(x+1)}\)
\(=\lim\limits_{x\to 0}\frac{\sqrt{x+4}.\frac{3}{\sqrt[3]{(8+3x)^2}+2\sqrt[3]{8+3x}+4}+\frac{2}{\sqrt{4+x}+2}}{x+1}=1\)
giúp mình với ; lim\(\dfrac{4-3^n}{2.3^n+2}\),lim\(\dfrac{3^{n+1}-2^n}{2-2.3^n}\)
Tìm giới hạn của hàm số: \(\lim\limits_{x\rightarrow0}\)\(\dfrac{\text{}\sqrt{1+2x}.\sqrt[3]{1+3x}.\sqrt[4]{1+4x}-1}{x}\)
lim\(\dfrac{2\sqrt{x}-3\sqrt{x+3}+2}{x-1}\)
Tìm giới hạn :
\(L=\lim\limits_{x\rightarrow+\infty}\left(\sqrt[3]{\left(x+a_1\right)\left(x+a_1\right)\left(x+a_1\right)}-x\right)\)
giới hạn \(lim_{x\rightarrow3^+}\left(x-3\right)\sqrt{\frac{x+1}{x^2-9}}\) thuộc dạng nào ?
cho lim \(\dfrac{f\left(x\right)-5}{x-1}=4\) khi x->1 , lim \(\dfrac{g\left(x\right)-1}{x-1}=5\) khi x->1
tinh lim \(\dfrac{\sqrt{f\left(x\right)\times g\left(x\right)+4}-1}{x-1}\)khi x->1
tim a,b để lim \(\dfrac{ax+b-2\sqrt{x}}{x^3-3x+2}=\dfrac{1}{12}\) khi x->1
Tìm các giới hạn sau:
a) \(\lim\limits_{h\rightarrow0}\dfrac{2\left(x+h\right)^3-2x^3}{h}\)
b) \(\lim\limits_{x\rightarrow1}\dfrac{\left(x+x^2+...+x^{2021}\right)-2021}{x-1}\)
