\(\left|\frac{-\sqrt{2}}{\pi}\right|< 1\Rightarrow lim\left(\frac{-\sqrt{2}}{\pi}\right)^n=0\)
Bài 2: Giới hạn của hàm số
Các câu hỏi tương tự
tìm các giới hạn sau:
a; \(\lim\limits_{x\rightarrow\frac{\pi}{2}}\frac{sin\left(x-\frac{\pi}{4}\right)}{x}\)
b, \(\lim\limits_{x\rightarrow2}\frac{\sqrt[3]{3x^2-4}-\sqrt{3x-2}}{x+1}\)
c,\(\lim\limits_{x\rightarrow0}x^2sin\frac{1}{2}\)
tìm các giới hạn sau:
a; lim\(\frac{1+2+3+...+n}{3n^3}\)
b, lim \(\left(\frac{n+2}{n+1}+\frac{sin\text{n}}{2^n}\right)\)
c, lim \(\left(\sqrt{n^2-3n}-\sqrt{n^2+1}\right)\)
d,\(lim\left(\sqrt[3]{n^3+3n^2}-n\right)\)
tìm các giới hạn sau:
a, lim\(\frac{2^{5n+1}+3}{3^{5n+2}+1}\)
b, lim\(\frac{\left(-1\right)^n+4.3^n}{\left(-1\right)^{n+1}-2.3^n}\)
c, lim \(\left(1+n^2-\sqrt{n^4+n}\right)\)
d, lim \(\frac{2cosn^2}{n^2+1}\)
e, lim \(\left(\sqrt{n^2-2}-\sqrt[3]{n^3+2n}\right)\)
Tính giá trị giới hạn \(lim\left(x\rightarrow0\right)\dfrac{\left(x^2+\pi^{21}\right)\sqrt[7]{1-2x}-\pi^{21}}{x}\)
a. limlimits_{xrightarrow a}frac{xsqrt{x}-asqrt{a}}{sqrt{x}-sqrt{a}} e. limlimits_{xrightarrow0}frac{sqrt{1+x}-sqrt[3]{1+x}}{x}
b. limlimits_{xrightarrow1}frac{sqrt[n]{x}-1}{sqrt[m]{x}-1}left(m,nin Z^+right) f. limlimits_{xrightarrow2}frac{sqrt[3]{8x+11}-sqrt{x+7}}{x^2-3x+2}
c. limlimits_{xrightarrow1}frac{left(1-sqrt{x}right)left(1-sqrt[3]{x}right)left(1-sqrt[4]{x}right)left(1-sqrt[5]{x}right)}{left(1-xright)^4}...
Đọc tiếp
a. \(\lim\limits_{x\rightarrow a}\frac{x\sqrt{x}-a\sqrt{a}}{\sqrt{x}-\sqrt{a}}\) e. \(\lim\limits_{x\rightarrow0}\frac{\sqrt{1+x}-\sqrt[3]{1+x}}{x}\)
b. \(\lim\limits_{x\rightarrow1}\frac{\sqrt[n]{x}-1}{\sqrt[m]{x}-1}\left(m,n\in Z^+\right)\) f. \(\lim\limits_{x\rightarrow2}\frac{\sqrt[3]{8x+11}-\sqrt{x+7}}{x^2-3x+2}\)
c. \(\lim\limits_{x\rightarrow1}\frac{\left(1-\sqrt{x}\right)\left(1-\sqrt[3]{x}\right)\left(1-\sqrt[4]{x}\right)\left(1-\sqrt[5]{x}\right)}{\left(1-x\right)^4}\) g. \(\lim\limits_{x\rightarrow1}\frac{\sqrt[3]{3x-2}-\sqrt{2x-1}}{x^3-1}\)
d. \(\lim\limits_{x\rightarrow+\infty}\left(\sqrt{x+\sqrt{x+\sqrt{x}}}-\sqrt{x}\right)\) h. \(\lim\limits_{x\rightarrow1}\frac{\sqrt[3]{x+9}+\sqrt[3]{2x-6}}{x^3+1}\)
tìm các giới hạn sau
a,\(lim\frac{\left(n^2+1\right)\left(2n+3\right)}{\sqrt{n^4-n^2+1}}\)
b, lim\(\frac{\left(-3^n-6^n\right)}{\left(-3\right)^{n+1}-5^{n+1}}\)
c,lim\(\left(\sqrt{n^4+1}+n-1\right)\)
d, \(\sqrt[3]{1+2n-n^3}\)
1, limlimits_{xrightarrow1}frac{2x^2-3x+1}{x^3-x^2-x+1}
2, limlimits_{xrightarrow2}frac{x-sqrt{x+2}}{sqrt{4x+1}-3}
3, limlimits_{xrightarrow0}frac{1-sqrt[3]{x-1}}{x}
4, limlimits_{xrightarrow-infty}frac{x^2-5x+1}{x^2-2}
5, limlimits_{xrightarrow+infty}frac{2x^2-4}{x^3+3x^2-9}
6, limlimits_{xrightarrow2^-}frac{2x-1}{x-2}
7, limlimits_{xrightarrow3^+}frac{8+x-x^2}{x-3}
8, limlimits_{xrightarrow-infty}left(8+4x-x^3right)
9, limlimits_{xrightarrow-1}frac{sq...
Đọc tiếp
1, \(\lim\limits_{x\rightarrow1}\frac{2x^2-3x+1}{x^3-x^2-x+1}\)
2, \(\lim\limits_{x\rightarrow2}\frac{x-\sqrt{x+2}}{\sqrt{4x+1}-3}\)
3, \(\lim\limits_{x\rightarrow0}\frac{1-\sqrt[3]{x-1}}{x}\)
4, \(\lim\limits_{x\rightarrow-\infty}\frac{x^2-5x+1}{x^2-2}\)
5, \(\lim\limits_{x\rightarrow+\infty}\frac{2x^2-4}{x^3+3x^2-9}\)
6, \(\lim\limits_{x\rightarrow2^-}\frac{2x-1}{x-2}\)
7, \(\lim\limits_{x\rightarrow3^+}\frac{8+x-x^2}{x-3}\)
8, \(\lim\limits_{x\rightarrow-\infty}\left(8+4x-x^3\right)\)
9, \(\lim\limits_{x\rightarrow-1}\frac{\sqrt[3]{x}+1}{\sqrt{x^2+3}-2}\)
10, \(\lim\limits_{x\rightarrow-\infty}\frac{\left(2x^2+1\right)^2\left(5x+3\right)}{\left(2x^3-1\right)\left(x+1\right)^2}\)
11, \(\lim\limits_{x\rightarrow-\infty}\frac{\sqrt{x^2+2x}}{x+3}\)
12, \(\lim\limits_{x\rightarrow1}\frac{\sqrt{5-x^3}-\sqrt[3]{x^2+7}}{x^2-1}\)
13, \(\lim\limits_{x\rightarrow0}\frac{\sqrt[3]{x+1}+\sqrt{x+4}-3}{x}\)
14, \(\lim\limits_{x\rightarrow0}\frac{\left(x^2+2020\right)\sqrt{1+3x}-2020}{x}\)
15, \(\lim\limits_{x\rightarrow+\infty}\left(2x-\sqrt{4x^2-3}\right)\)
16, \(\lim\limits_{x\rightarrow a}\frac{x^2-\left(a+1\right)x+a}{x^3-a^3}\)
17, \(\lim\limits_{x\rightarrow1}\frac{x^n-nx+n-1}{\left(x-1\right)^2}\)
18, \(f\left(x\right)=\left\{{}\begin{matrix}\frac{x^2-2x}{8-x^3}\\\frac{x^4-16}{x-2}\end{matrix}\right.\) khi x>2,khi x<2 tại x=2
a/ ^{lim}_{x-0}frac{sqrt{1+x}-sqrt[3]{1+x}}{x}
b/^{lim}_{x-1}left(frac{1}{1-x}-frac{1}{1-x^3}right)
c/ ^{lim}_{x-+infty}left(sqrt[3]{2x-1}-sqrt[3]{2x+1}right)
d/ ^{lim}_{x--infty}left(sqrt[3]{3x^3-1}+sqrt{x^2+2}right)
e/^{lim}_{x-2}left(frac{1}{x^2-3x+2}+frac{1}{x^2-5x+6}right)
f/ ^{lim}_{x-0^{+-}}left(frac{2x}{sqrt{4x^2+x^3}}right)
Đọc tiếp
a/ \(^{lim}_{x->0}\frac{\sqrt{1+x}-\sqrt[3]{1+x}}{x}\)
b/\(^{lim}_{x->1}\left(\frac{1}{1-x}-\frac{1}{1-x^3}\right)\)
c/ \(^{lim}_{x->+\infty}\left(\sqrt[3]{2x-1}-\sqrt[3]{2x+1}\right)\)
d/ \(^{lim}_{x->-\infty}\left(\sqrt[3]{3x^3-1}+\sqrt{x^2+2}\right)\)
e/\(^{lim}_{x->2}\left(\frac{1}{x^2-3x+2}+\frac{1}{x^2-5x+6}\right)\)
f/ \(^{lim}_{x->0^{+-}}\left(\frac{2x}{\sqrt{4x^2+x^3}}\right)\)
Tính giá trị giới hạn lim (x → 0) \(\dfrac{\left(x^2+\Pi^{21}\right)\sqrt[7]{1-2x}-\Pi^{21}}{x}\) là: