Lời giải:
\(\lim\limits_{x\to 3}\left(\frac{1}{x}-\frac{1}{3}\right).\frac{1}{(x-3)^3}=\lim\limits_{x\to 3}\frac{3-x}{3x(x-3)^3}=\lim\limits_{x\to 3}\frac{-1}{3x(x-3)^2}=-\infty \)
Bài 2: Giới hạn của hàm số
Các câu hỏi tương tự
Tính các giới hạn sau đây :
L_1limfrac{x^3+3x^2-2x}{x^5+4x}left(xrightarrow0right)
L_2limfrac{x^3-3x+2}{left(4-2xright)^3}left(xrightarrow+inftyright)
L_3limfrac{2x^2+3x+1}{x^2+x}left(xrightarrow-1right)
L_4limfrac{x^2-4x+1}{4-x^2}left(xrightarrow2right)
L_5limfrac{sqrt{x+1}-2}{x-2}left(xrightarrow3right)
L_6limfrac{sqrt{x+3}-x-1}{x^2-1}left(xrightarrow1right)
L_7limleft(sqrt{x^2+x+1}-x+1right)left(xrightarrow+inftyright)
L_8limleft(sqrt{x^2+x+1}-3x+2right)left(xrightarrow-...
Đọc tiếp
Tính các giới hạn sau đây :
\(L_1=lim\frac{x^3+3x^2-2x}{x^5+4x}\left(x\rightarrow0\right)\)
\(L_2=lim\frac{x^3-3x+2}{\left(4-2x\right)^3}\left(x\rightarrow+\infty\right)\)
\(L_3=lim\frac{2x^2+3x+1}{x^2+x}\left(x\rightarrow-1\right)\)
\(L_4=lim\frac{x^2-4x+1}{4-x^2}\left(x\rightarrow2\right)\)
\(L_5=lim\frac{\sqrt{x+1}-2}{x-2}\left(x\rightarrow3\right)\)
\(L_6=lim\frac{\sqrt{x+3}-x-1}{x^2-1}\left(x\rightarrow1\right)\)
\(L_7=lim\left(\sqrt{x^2+x+1}-x+1\right)\left(x\rightarrow+\infty\right)\)
\(L_8=lim\left(\sqrt{x^2+x+1}-3x+2\right)\left(x\rightarrow-\infty\right)\)
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/ \(^{lim}_{x->0^{+-}}\left(\frac{2x}{\sqrt{4x^2+x^3}}\right)\)
Bài 1
a. limlimits_{xrightarrow-infty}left(sqrt[3]{x^3-x^2}-xright)
b. limlimits_{xrightarrow+infty}left(sqrt[3]{x^3+5x^2}-sqrt[3]{x^3+8x}right)
c. limlimits_{xrightarrow+infty}left(sqrt[3]{x^3+1}-xright)
Bài 2
a. limlimits_{xrightarrow1^-}left(frac{2}{x^2-1}-frac{1}{x-1}right)
b. limlimits_{xrightarrow1^+}left(frac{1}{1-x}-frac{3}{1-x^3}right)
c. limlimits_{xrightarrow2^+}left(frac{1}{x^2-3x+2}-frac{1}{x^2-5x+6}right)
Đọc tiếp
Bài 1
a. \(\lim\limits_{x\rightarrow-\infty}\left(\sqrt[3]{x^3-x^2}-x\right)\)
b. \(\lim\limits_{x\rightarrow+\infty}\left(\sqrt[3]{x^3+5x^2}-\sqrt[3]{x^3+8x}\right)\)
c. \(\lim\limits_{x\rightarrow+\infty}\left(\sqrt[3]{x^3+1}-x\right)\)
Bài 2
a. \(\lim\limits_{x\rightarrow1^-}\left(\frac{2}{x^2-1}-\frac{1}{x-1}\right)\)
b. \(\lim\limits_{x\rightarrow1^+}\left(\frac{1}{1-x}-\frac{3}{1-x^3}\right)\)
c. \(\lim\limits_{x\rightarrow2^+}\left(\frac{1}{x^2-3x+2}-\frac{1}{x^2-5x+6}\right)\)
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. \(\lim\limits_{x\rightarrow1}\frac{\sqrt[3]{x+9}+\sqrt[3]{2x-6}}{x^3+1}\)
Bài 1
a. limlimits_{xrightarrow-1}frac{x^5+1}{x^3+1}
b. limlimits_{xrightarrow1}frac{x^6-5x^5+x}{left(1-xright)^2}
c. limlimits_{xrightarrow0}frac{left(1+xright)left(1+2xright)left(1+3xright)-1}{x}
d. limlimits_{xrightarrow0}frac{left(1+xright)^5-left(1+xright)}{x^5+x^2}
Bài 2
a. limlimits_{xrightarrow1}frac{x^m-1}{x^n-1}
b. limlimits_{xrightarrow a}frac{x-a}{x^n-a^n}left(nin Z^+,ane0right)
c. limlimits_{xrightarrow0}frac{x+x^2+...+x^n-n}{x-1}
d. limlimits_{xrightarrow0}frac{lef...
Đọc tiếp
Bài 1
a. \(\lim\limits_{x\rightarrow-1}\frac{x^5+1}{x^3+1}\)
b. \(\lim\limits_{x\rightarrow1}\frac{x^6-5x^5+x}{\left(1-x\right)^2}\)
c. \(\lim\limits_{x\rightarrow0}\frac{\left(1+x\right)\left(1+2x\right)\left(1+3x\right)-1}{x}\)
d. \(\lim\limits_{x\rightarrow0}\frac{\left(1+x\right)^5-\left(1+x\right)}{x^5+x^2}\)
Bài 2
a. \(\lim\limits_{x\rightarrow1}\frac{x^m-1}{x^n-1}\)
b. \(\lim\limits_{x\rightarrow a}\frac{x-a}{x^n-a^n}\left(n\in Z^+,a\ne0\right)\)
c. \(\lim\limits_{x\rightarrow0}\frac{x+x^2+...+x^n-n}{x-1}\)
d. \(\lim\limits_{x\rightarrow0}\frac{\left(1+x\right)\left(1+2x\right)...\left(1+nx\right)-1}{x}\)
Bài 1
a. limlimits_{xrightarrow-infty}frac{sqrt{4x^2}+1}{3x-1}
b. limlimits_{xrightarrow+infty}frac{sqrt{9x^2+x+1}-sqrt{4x^2+2x+1}}{x+1}
c. limlimits_{xrightarrow+infty}frac{sqrt{x+2x+3}+4x+1}{sqrt{4x^2+1}+2-x}
d. limlimits_{xrightarrow+infty}frac{3x-2sqrt{x}+sqrt{x^4-5x}}{2x^2+4x-5}
Bài 2
a. limlimits_{xrightarrow-infty}frac{2x+1}{x-1}
b. limlimits_{xrightarrow-infty}frac{2x^3+3}{x^3-2x^2+1}
c. limlimits_{xrightarrow+infty}frac{left(3x^2+1right)left(5x+3right)}{left(2x^3-1r...
Đọc tiếp
Bài 1
a. \(\lim\limits_{x\rightarrow-\infty}\frac{\sqrt{4x^2}+1}{3x-1}\)
b. \(\lim\limits_{x\rightarrow+\infty}\frac{\sqrt{9x^2+x+1}-\sqrt{4x^2+2x+1}}{x+1}\)
c. \(\lim\limits_{x\rightarrow+\infty}\frac{\sqrt{x+2x+3}+4x+1}{\sqrt{4x^2+1}+2-x}\)
d. \(\lim\limits_{x\rightarrow+\infty}\frac{3x-2\sqrt{x}+\sqrt{x^4-5x}}{2x^2+4x-5}\)
Bài 2
a. \(\lim\limits_{x\rightarrow-\infty}\frac{2x+1}{x-1}\)
b. \(\lim\limits_{x\rightarrow-\infty}\frac{2x^3+3}{x^3-2x^2+1}\)
c. \(\lim\limits_{x\rightarrow+\infty}\frac{\left(3x^2+1\right)\left(5x+3\right)}{\left(2x^3-1\right)\left(x+4\right)}\)
Bài 1
a. limlimits_{xrightarrow-1}frac{x^5+1}{x^3+1}
b. limlimits_{xrightarrow1}frac{4x^6-5x^5+x}{left(1-xright)^2}
c. limlimits_{xrightarrow0}frac{left(1+xright)left(1+2xright)left(1+3xright)-1}{x}
d. limlimits_{xrightarrow0}frac{left(1+xright)^5-left(1+5xright)}{x^5+x^2}
Bài 2
a. limlimits_{xrightarrow1}frac{x^m-1}{x^n-1}
b. limlimits_{xrightarrow a}frac{x-a}{x^n-a^n}left(nin Z^+,ane0right)
Đọc tiếp
Bài 1
a. \(\lim\limits_{x\rightarrow-1}\frac{x^5+1}{x^3+1}\)
b. \(\lim\limits_{x\rightarrow1}\frac{4x^6-5x^5+x}{\left(1-x\right)^2}\)
c. \(\lim\limits_{x\rightarrow0}\frac{\left(1+x\right)\left(1+2x\right)\left(1+3x\right)-1}{x}\)
d. \(\lim\limits_{x\rightarrow0}\frac{\left(1+x\right)^5-\left(1+5x\right)}{x^5+x^2}\)
Bài 2
a. \(\lim\limits_{x\rightarrow1}\frac{x^m-1}{x^n-1}\)
b. \(\lim\limits_{x\rightarrow a}\frac{x-a}{x^n-a^n}\left(n\in Z^+,a\ne0\right)\)
giới hạn \(lim\frac{2\sqrt{x+1}-4}{x-3}\) \(\left(x\rightarrow3\right)\) bằng :
A. 0
B. \(\frac{1}{2}\)
C. 8
D. \(+\infty\)