\(\lim\limits_{x\rightarrow-\infty}\dfrac{x^2+ax+5-x^2}{\sqrt{x^2+ax+5}-x}=\lim\limits_{x\rightarrow-\infty}\dfrac{\dfrac{ax}{x}+\dfrac{5}{x}}{-\sqrt{\dfrac{x^2}{x^2}+\dfrac{ax}{x^2}+\dfrac{5}{x^2}}-\dfrac{x}{x}}=\dfrac{-a}{2}\)
\(-\dfrac{a}{2}=5\Rightarrow a=-10\)
cho biết \(\lim\limits_{x\rightarrow-\infty}\dfrac{1-\sqrt{4x^2-x+5}}{a\left|x\right|+2}=\dfrac{2}{3}\). tính giá trị a?
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
cho a, b là sô thực biết lim(x-> \(+\infty\)) (\(ax+b-\sqrt{x^2-6x+2}\)) =3 . tinhs tong \(2ab+b+a^2\)
a) lim \(\dfrac{3x^4-2x^5}{5x^4+x+4}\)
x-> -∞
b) lim \(\dfrac{x-1}{\sqrt{x^2-1}}\)
x-> +∞
Với a >0 , lim (ax -\(\sqrt{a^2x^2-2x}\))
x-> +∞
biết \(\lim\limits_{x\rightarrow+\infty}\left(\dfrac{x^2+1}{x-2}+ax-b\right)=-5\). tìm a, b?
tính giá trị \(\lim\limits_{x\rightarrow-\infty}\dfrac{\sqrt{x^2-3x+6}+2x}{2x-3}\) ?
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 ..
có bao nhiêu giá trị nguyên a để \(lim\dfrac{\sqrt{an^3+n^2+1}-n\sqrt{2n+1}}{\sqrt{4n^3+3n}}\le\sqrt{2}\)
