\(=\lim\limits_{x\rightarrow+\infty}\frac{\left(x-1\right)\left(x-\sqrt{x^2+2}\right)\left(x+\sqrt{x^2+2}\right)}{x+\sqrt{x^2+2}}\)
\(=\lim\limits_{x\rightarrow+\infty}\frac{-2\left(x-1\right)}{x+\sqrt{x^2+2}}=\lim\limits_{x\rightarrow+\infty}\frac{-2\left(1-\frac{1}{x}\right)}{1+\sqrt{1+\frac{2}{x^2}}}=\frac{-2}{1+1}=-1\)
a) lim ( x2+x-1)
x-> -∞
b) lim ( \(\sqrt{x^2+x+1}-2\sqrt{x^2-x}+x\))
x-> +∞
c) lim x\(\left(\sqrt{x^2+2x}-2\sqrt{x^2+x}+x\right)\)
x-> +∞
a) lim ( \(\sqrt{x^2-x+1}-\sqrt{x^2+x+1}\)
x-> +∞
b) lim \(\dfrac{\sqrt{4x+1}-3}{x^2-4}\)
x-> 2
c) lim \(\dfrac{\sqrt{2x+5}-1}{x^2-4}\)
x-> -2
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
a) lim (2x+ \(\sqrt{4x^2-x+1}\))
x-> -∞
b) lim x\(\left(\sqrt{4x^2+1}-x\right)\)
x-> -∞
a) lim \(\dfrac{x\sqrt{x^2+1}-2x+1}{^3\sqrt{2x^3-2}+1}\)
x-> -∞
b) lim \(\dfrac{\left(2x+1\right)^3\left(x+2\right)^4}{\left(3-2x\right)^7}\)
x-> -∞
c) lim \(\dfrac{\sqrt{4x^2+x}+^3\sqrt{8x^3+x-1}}{^4\sqrt{x^4+3}}\)
x-> +∞
a) lim \(\dfrac{3x^4-2x^5}{5x^4+x+4}\)
x-> -∞
b) lim \(\dfrac{x-1}{\sqrt{x^2-1}}\)
x-> +∞
a) lim \(\dfrac{2x-\sqrt{3x^2+2}}{5x+\sqrt{x^2+2}}\)
x-> +∞
b) lim \(\sqrt{\dfrac{x^2+1}{2x^4+x^2-3}}\)
x-> ∞
cho \(\lim\limits_{x\rightarrow-\infty}\dfrac{a\sqrt{x^2+1}+2017}{x+2018}=\dfrac{1}{2}\); \(\lim\limits_{x\rightarrow+\infty}\left(\sqrt{x^2+bx+1}-x\right)=2\). Tính P=4a+b
Tìm giơi han:
a) lim (x-> \(+\infty\)) \(\dfrac{\sqrt{x^2+1}+x}{5-2x}\)
b) lim (x->4) \(\left(\dfrac{\sqrt{15x+4}-\sqrt{x-3}-3}{-x+4}\right)\)
sorry, e k bt nhâp lim ..
lim (2+x) . \(\sqrt{\dfrac{x-1}{x^4+x^2+1}}\)
x-> + ∞
