\(\lim\limits_{x\rightarrow-\infty}\frac{-2x^5+x^4-3}{3x^2-7}=\lim\limits_{x\rightarrow-\infty}\frac{-2x^3+x-\frac{3}{x^2}}{3-\frac{7}{x^2}}=-\frac{2}{3}.\left(-\infty\right)=+\infty\)
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 :
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) \(\lim\limits_{x\rightarrow+\infty}\dfrac{\sqrt{x^2+1}+x}{5-2x}\)
BÀI 3. Tính các giới hạn sau:
a) \(\lim\limits_{x\rightarrow-\infty}\dfrac{2x^3-5x^2+1}{7x^2-x+4}\)
b) \(\lim\limits_{x\rightarrow+\infty}x\sqrt{\dfrac{x^2+2x+3}{3x^4+4x^2-5}}\)
Tính các giới hạn sau đây :
\(L_1=lim\frac{x^3+3x^2-2x}{x^5+4x}\left(x\rightarrow0\right)\)
\(L_2=lim\frac{x^3-3x+2}{\left(4-2x\right)^3}\left(x\rightarrow+\infty\right)\)
\(L_3=lim\frac{2x^2+3x+1}{x^2+x}\left(x\rightarrow-1\right)\)
\(L_4=lim\frac{x^2-4x+1}{4-x^2}\left(x\rightarrow2\right)\)
\(L_5=lim\frac{\sqrt{x+1}-2}{x-2}\left(x\rightarrow3\right)\)
\(L_6=lim\frac{\sqrt{x+3}-x-1}{x^2-1}\left(x\rightarrow1\right)\)
\(L_7=lim\left(\sqrt{x^2+x+1}-x+1\right)\left(x\rightarrow+\infty\right)\)
\(L_8=lim\left(\sqrt{x^2+x+1}-3x+2\right)\left(x\rightarrow-\infty\right)\)
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→\(+\infty\)
giới hạn \(lim\frac{\sqrt{x^2+1}+x}{3x+5}\) \(\left(x\rightarrow+\infty\right)\) bằng :
A. \(\frac{2}{3}\)
B. \(\frac{1}{3}\)
C. 0
D. \(+\infty\)
\(\lim\limits_{x\rightarrow-\infty}\left(3x^3+5x^2-9\sqrt{2}x-2017\right)\)
\(\lim\limits_{x\rightarrow+\infty}\left(\sqrt{x^2+x+1}-\sqrt[3]{2x^3+x-1}\right)\)
\(\lim\limits_{x\rightarrow-\infty}\left(x-\sqrt{x^2+x+1}\right)\)
\(\lim\limits_{x\rightarrow-\infty}\left(\sqrt[3]{x^3+x^2+1}+\sqrt{x^2+x+1}\right)\)
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. \(\lim\limits_{x\rightarrow+\infty}\left(\sqrt[3]{x^3+3x^2}-\sqrt{x^2-2x}\right)\)
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) \(\lim\limits_{x\rightarrow-\infty}\dfrac{\left(x^2-1\right)\left(1-2x\right)^5}{x^7+x+3}\)
