\(\lim\limits_{x\rightarrow\infty}\frac{\left(x-1\right)^2\left(7x+2\right)^2}{\left(2x+1\right)^4}=\lim\limits_{x\rightarrow\infty}\frac{x^2\left(1-\frac{1}{x}\right)^2.x^2\left(7+\frac{2}{x}\right)^2}{x^4\left(2+\frac{1}{x}\right)^4}=\frac{1.7^2}{2^4}=\frac{49}{16}\)
Câu 1:
a, limx→+∞ (\(\sqrt{x+1}-\sqrt{x}\))
b, limx→+∞ (\(\sqrt{x+\sqrt{x}}-\sqrt{x}\))
c, limx→-∞ (\(\sqrt{3x^2+x+1}+x\sqrt{3}\))
d, limx→+∞ (\(\sqrt{x^2+2x+4}-\sqrt{x^2-2x+4}\))
Tính các giới hạn sau:
Câu 1:
a, limx→\(\pm\)∞ \(\dfrac{\left(2x-3\right)^2\left(4x+7\right)^3}{\left(3x-4\right)^2\left(5x^2-1\right)}\)
b, limx→\(\pm\)∞ \(\dfrac{\sqrt[3]{x^3+2x^2+x}}{2x-2}\)
c, limx→\(\pm\)∞ \(\dfrac{\sqrt[3]{\left(x^3+2x^2\right)^2}+x^3\sqrt{x^3+2x^2}+x^2}{3x^2-2x}\)
d, limx→+∞ \(\dfrac{\left(2-3x\right)^3\left(x+1\right)^2}{1-4x^5}\)
e, limx→+∞ \(\dfrac{\left(2x-3\right)^{20}\left(3x+2\right)^{20}}{\left(2x+1\right)^{50}}\)
g, limx→+∞ \(\dfrac{\left(2x-3\right)^3\left(4x^5+7\right)^9}{11x^{47}-8}\)
Bài 1 tìm các giới hạn sau :
a, lim 2x²-3x-2/x-2
(limx->2)
b, lim x³-3x²+5x-3/x²-1
(limx->1)
c, limx²+2x/x²+4x+4
(limx->2)
d, limx³-x²-x+1/x²-3x+2
(lim x->1)
e, limx³-5x²+3x+9/x4-8x²-9
(lim x->1)
f, lim x4-1/x³-2x²+3
(limx->-1)
g, limx²+2x-3/2x²-x-1
(limx->1)
h,lim x³-3x+2/4-x²
(lim x->-2)
i, lim4x6-5x5+1/x²-1
(lim x->1)
k, lim x mũ m -1/ x mũ n -1
(lim x->1)m, n thuộc N
Câu 1:
a, limx→-∞ \(\dfrac{x+\sqrt{x^2+2}}{\sqrt{8x^2+5x+2}}\)
b, limx→-∞ \(\dfrac{\sqrt{x^2+2x}+3x}{\sqrt{4x^2+1}-x+2}\)
c, limx→-∞ \(\dfrac{x+\sqrt{x^2+x}}{3x-\sqrt{x^2+1}}\)
d, limx→-∞ \(\dfrac{\sqrt{x^2+x+2}+3x}{\sqrt{4x^2+1}-x+1}\)
limx→0\(\dfrac{\left(x^2+\pi^2\right)\sqrt[7]{1-2x}-x^2}{x}\)
limx->1(căn(x+8)+căn(2x+2)-5x)/(x-1)
BÀI 3. Tính các giới hạn sau:
a) \(\lim\limits_{x\rightarrow-\infty}\dfrac{2x^3-5x^2+1}{7x^2-x+4}\)
b) \(\lim\limits_{x\rightarrow+\infty}x\sqrt{\dfrac{x^2+2x+3}{3x^4+4x^2-5}}\)
limX tiến tới 1 \(\frac{\sqrt{2X+2}-\sqrt{3X+1}}{X-1}\)
limx→-∞
\(\dfrac{1}{4x-2}\sqrt{\dfrac{8x^3+x-1}{x+4}}\)
giúp mình với mn ơi=(((