Bài 2: Giới hạn của hàm số
Các câu hỏi tương tự
Giá trị của các giới hạn :
a, lim\(\left(\sqrt[3]{3x^3-1}+\sqrt{x^2+1}\right)\) khi x→\(-\infty\)
b, lim\(\left(\sqrt{x^2+x}-\sqrt[3]{x^3-x^2}\right)\) khi x→\(+\infty\)
c, lim\(\left(\sqrt[3]{2x-1}-\sqrt[3]{2x+1}\right)\) khi x→\(+\infty\)
Tính các giới hạn sau :
a) limlimits_{xrightarrow-3}dfrac{x+3}{x^2+2x-3}
b) limlimits_{xrightarrow0}dfrac{left(1+xright)^3-1}{x}
c) limlimits_{xrightarrow+infty}dfrac{x-1}{x^2-1}
d) limlimits_{xrightarrow5}dfrac{x-5}{sqrt{x}-sqrt{5}}
e) limlimits_{xrightarrow+infty}dfrac{x-5}{sqrt{x}+sqrt{5}}
f) limlimits_{xrightarrow-2}dfrac{sqrt{x^2+5}-3}{x+2}
g) limlimits_{xrightarrow1}dfrac{sqrt{x}-1}{sqrt{x+3}-2}
h) limlimits_{xrightarrow+infty}dfrac{1-2x+3x^3}{x^3-9}
i) limlimits_{xrightarrow0}dfr...
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Tính các giới hạn sau :
a) \(\lim\limits_{x\rightarrow-3}\dfrac{x+3}{x^2+2x-3}\)
b) \(\lim\limits_{x\rightarrow0}\dfrac{\left(1+x\right)^3-1}{x}\)
c) \(\lim\limits_{x\rightarrow+\infty}\dfrac{x-1}{x^2-1}\)
d) \(\lim\limits_{x\rightarrow5}\dfrac{x-5}{\sqrt{x}-\sqrt{5}}\)
e) \(\lim\limits_{x\rightarrow+\infty}\dfrac{x-5}{\sqrt{x}+\sqrt{5}}\)
f) \(\lim\limits_{x\rightarrow-2}\dfrac{\sqrt{x^2+5}-3}{x+2}\)
g) \(\lim\limits_{x\rightarrow1}\dfrac{\sqrt{x}-1}{\sqrt{x+3}-2}\)
h) \(\lim\limits_{x\rightarrow+\infty}\dfrac{1-2x+3x^3}{x^3-9}\)
i) \(\lim\limits_{x\rightarrow0}\dfrac{1}{x^2}\left(\dfrac{1}{x^2+1}-1\right)\)
j) \(\lim\limits_{x\rightarrow-\infty}\dfrac{\left(x^2-1\right)\left(1-2x\right)^5}{x^7+x+3}\)
Tìm giới hạn của các hàm số sau :
a) fleft(xright)dfrac{x^2-2x-3}{x-1} khi xrightarrow3
b) hleft(xright)dfrac{2x^3+15}{left(x-2right)^2} khi xrightarrow-2
c) kleft(xright)sqrt{4x^2-x+1} khi xrightarrow-infty
d) fleft(xright)x^3+x^2+1 khi xrightarrow-infty
e) hleft(xright)dfrac{x-15}{x+2} khi xrightarrow-2^+ và khi xrightarrow-2^-
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Tìm giới hạn của các hàm số sau :
a) \(f\left(x\right)=\dfrac{x^2-2x-3}{x-1}\) khi \(x\rightarrow3\)
b) \(h\left(x\right)=\dfrac{2x^3+15}{\left(x-2\right)^2}\) khi \(x\rightarrow-2\)
c) \(k\left(x\right)=\sqrt{4x^2-x+1}\) khi \(x\rightarrow-\infty\)
d) \(f\left(x\right)=x^3+x^2+1\) khi \(x\rightarrow-\infty\)
e) \(h\left(x\right)=\dfrac{x-15}{x+2}\) khi \(x\rightarrow-2^+\) và khi \(x\rightarrow-2^-\)
\(\lim\limits_{x\rightarrow-\infty}\left(3x^3+5x^2-9\sqrt{2}x-2017\right)\)
\(\lim\limits_{x\rightarrow+\infty}\left(\sqrt{x^2+x+1}-\sqrt[3]{2x^3+x-1}\right)\)
\(\lim\limits_{x\rightarrow-\infty}\left(x-\sqrt{x^2+x+1}\right)\)
\(\lim\limits_{x\rightarrow-\infty}\left(\sqrt[3]{x^3+x^2+1}+\sqrt{x^2+x+1}\right)\)
1, Tính:
a, \(\lim\limits_{x\rightarrow-2}\dfrac{x^3+2x^2}{\sqrt{x^2+4x+4}}\)
b, \(\lim\limits_{x\rightarrow+\infty}\left(\sqrt{x+\sqrt{x+1}}-\sqrt{x}\right)\)
c, \(\lim\limits_{x\rightarrow-\infty}\left(\sqrt{x^2-x}+1+\sqrt[3]{x^3+2}\right)\)
a. \(\lim\limits_{x\rightarrow+\infty}\left(\sqrt{x+\sqrt{x+\sqrt{x}}}-\sqrt{x-\sqrt{x-\sqrt{x}}}\right)\)
b. \(\lim\limits_{x\rightarrow+\infty}x\left(\sqrt{x^2+2x}-2\sqrt{x^2+x}+x\right)\)
c. \(\lim\limits_{x\rightarrow+\infty}\left(\sqrt[3]{x^3+3x^2}-\sqrt{x^2-2x}\right)\)
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...
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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. \(\lim\limits_{x\rightarrow+\infty}\frac{\left(3x^2+1\right)\left(5x+3\right)}{\left(2x^3-1\right)\left(x+4\right)}\)
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-...
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Tính các giới hạn sau đây :
\(L_1=lim\frac{x^3+3x^2-2x}{x^5+4x}\left(x\rightarrow0\right)\)
\(L_2=lim\frac{x^3-3x+2}{\left(4-2x\right)^3}\left(x\rightarrow+\infty\right)\)
\(L_3=lim\frac{2x^2+3x+1}{x^2+x}\left(x\rightarrow-1\right)\)
\(L_4=lim\frac{x^2-4x+1}{4-x^2}\left(x\rightarrow2\right)\)
\(L_5=lim\frac{\sqrt{x+1}-2}{x-2}\left(x\rightarrow3\right)\)
\(L_6=lim\frac{\sqrt{x+3}-x-1}{x^2-1}\left(x\rightarrow1\right)\)
\(L_7=lim\left(\sqrt{x^2+x+1}-x+1\right)\left(x\rightarrow+\infty\right)\)
\(L_8=lim\left(\sqrt{x^2+x+1}-3x+2\right)\left(x\rightarrow-\infty\right)\)
Tính :
a) \(\lim\limits_{x\rightarrow+\infty}\left(x^4-x^2+x-1\right)\)
b) \(\lim\limits_{x\rightarrow-\infty}\left(-2x^3+3x^2-5\right)\)
c) \(\lim\limits_{x\rightarrow-\infty}\sqrt{x^2-2x+5}\)
d) \(\lim\limits_{x\rightarrow+\infty}\dfrac{\sqrt{x^2+1}+x}{5-2x}\)