\(\lim\limits\frac{\sqrt{4n^2+1}-\sqrt{n+2}}{2n-3}=\lim\limits\frac{\sqrt{4+\frac{1}{n^2}}-\sqrt{\frac{1}{n}+\frac{2}{n^2}}}{2-\frac{3}{n}}=\frac{\sqrt{4}-0}{2}=1\)
Cho lim \(\left(\frac{\sqrt{x^2+x+2}-\sqrt[3]{2x^3+5x+1}}{x^2-1}\right)=\frac{a}{b}\) \(\left(x\rightarrow\infty\right)\) ( \(\frac{a}{b}\) là phân số tối giản , a , b là số nguyên ) . Tính tổng \(L=a^2+b^2\)
A. 150
B. 143
C. 140
D. 145
Tìm giới hạn D = lim \(\left(\sqrt[3]{x^3+x^2+1}+\sqrt{x^2+x+1}\right)\) \(\left(x\rightarrow-\infty\right)\)
A. \(+\infty\)
B. \(-\infty\)
C. \(-\frac{1}{6}\)
D. 0
Tính lim \(x\left(\sqrt{x^2+2x}-\sqrt[3]{x^3+3x^2}\right)\) \(\left(x\rightarrow+\infty\right)\)
A. \(\frac{1}{2}\)
B. 0
C. \(+\infty\)
D. \(-\infty\)
Tìm giới hạn :
A = lim \(\left(\sqrt{x^2+x+1}-2\sqrt{x^2-x+x}\right)\)
A. +\(\infty\)
B. \(-\infty\)
C. \(\frac{3}{2}\)
D. 0
help me !!!!!!
Tính các giới hạn sau (\(n\rightarrow+\infty\) )
a) \(\lim\limits\dfrac{\left(-3\right)^n+2.5^n}{1-5^n}\)
b) \(\lim\limits\dfrac{1+2+3+....+n}{n^2+n+1}\)
c) \(\lim\limits\left(\sqrt{n^2+2n+1}-\sqrt{n^2+n-1}\right)\)
Tính 1) \(lim\frac{\sqrt{n}-2}{n+\sqrt{n}+1}\)
2) \(lim\frac{\sqrt[3]{n^3+n}+2}{n+2}\)
3)\(lim\frac{\sqrt[3]{n^3+1}-1}{\sqrt{n^2+3}-2}\)
\(\lim\limits_{x\rightarrow+\infty}\left(\sqrt{x^2+x+1}-\sqrt[3]{2x^3+x-1}\right)\)
\(\lim\limits_{x\rightarrow+\infty}\left(\sqrt{4x^2+x+1}-2x\right)\)
\(\lim\limits_{x\rightarrow-\infty}\left(\sqrt[3]{x^3+x^2+1}+\sqrt{x^2+x+1}\right)\)
\(\lim\limits_{x\rightarrow+\infty}\left(\sqrt{x^2+x+1}-2\sqrt{x^2-x}+x\right)\)
\(\lim\limits_{x\rightarrow+\infty}x\left(\sqrt{x^2+2x}-2\sqrt{x^2+x}+x\right)\)
Tìm giới hạn A = lim \(\left(\sqrt{x^2+x+1}-2\sqrt{x^2-x}+x\right)\) \(\left(x\rightarrow+\infty\right)\)
A. \(+\infty\)
B. \(-\infty\)
C. \(\frac{3}{2}\)
D. 0
\(\lim\limits_{x\rightarrow+\infty}\dfrac{2x-\sqrt{3x^2+2}}{5x+\sqrt{x^2+1}}\)
\(\lim\limits_{x\rightarrow+\infty}\sqrt{\dfrac{x^2+1}{2x^4+x^2-3}}\)
\(\lim\limits_{x\rightarrow-\infty}\dfrac{\sqrt[3]{1+x^4+x^6}}{\sqrt{1+x^3+x^4}}\)