Trong các giới hạn sau , giới hạn nào không tồn tại ?
A. \(lim\frac{x+1}{\sqrt{x-2}}\left(x\rightarrow1\right)\)
B. \(lim\frac{x+1}{\sqrt{-x+2}}\left(x\rightarrow-1\right)\)
C. \(lim\frac{x+1}{\sqrt{2-x}}\left(x\rightarrow1\right)\)
D. \(lim\frac{x+1}{\sqrt{2+x}}\left(x\rightarrow-1\right)\)
Tìm các giới hạn sau :
a) \(\lim\limits_{x\rightarrow0}\dfrac{\sqrt{x^2+1}-1}{4-\sqrt{x^2+16}}\)
b) \(\lim\limits_{x\rightarrow1}\dfrac{x-\sqrt{x}}{\sqrt{x}-1}\)
c) \(\lim\limits_{x\rightarrow+\infty}\dfrac{2x^4+5x-1}{1-x^2+x^4}\)
d) \(\lim\limits_{x\rightarrow-\infty}\dfrac{x+\sqrt{4x^2-x+1}}{1-2x}\)
e) \(\lim\limits_{x\rightarrow+\infty}x\left(\sqrt{x^2+1}-x\right)\)
f) \(\lim\limits_{x\rightarrow2^+}\left(\dfrac{1}{x^2-4}-\dfrac{1}{x-2}\right)\)
\(\lim\limits_{x\rightarrow-\infty}\dfrac{\sqrt[3]{3x^3+1}-\sqrt{2x^2+x+1}}{\sqrt[4]{4x^4+2}}\)
\(\lim\limits_{x\rightarrow+\infty}\dfrac{\left(2x+1\right)^3\left(x+2\right)^4}{\left(3-2x\right)^7}\)
\(\lim\limits_{x\rightarrow+\infty}\dfrac{\sqrt{4x^2-3x+4}-2x}{\sqrt{x^2+x+1}-x}\)
\(\lim\limits_{x\rightarrow-\infty}\left(x-\sqrt{x^2+x+1}\right)\)
\(\lim\limits_{x\rightarrow\pm\infty}\left(\sqrt{x^2+3x+1}-\sqrt{x^2-x+1}\right)\)
\(\lim\limits_{x\rightarrow+\infty}\left(\sqrt[3]{8x^3+2x}-2x\right)\)
\(\lim\limits_{x\rightarrow+\infty}\left(\sqrt[4]{16x^4+3x+1}-\sqrt{4x^2+2}\right)\)
\(\lim\limits_{x\rightarrow+\infty}\left(\sqrt{x^2+1}+\sqrt{x^2-x}-2x\right)\)
\(\lim\limits_{x\rightarrow+\infty}\left(\sqrt{x^2-x+1}-x\right)\)
\(\lim\limits_{x\rightarrow-\infty}x\left(\sqrt{4x^2+1}-x\right)\)
\(\lim\limits_{x\rightarrow-\infty}\left(4x^5-3x^3+x+1\right)\)
\(\lim\limits_{x\rightarrow+\infty}\sqrt{x^4-x^3+x^2-x}\)
Tìm các giới hạn sau :
a) \(\lim\limits_{x\rightarrow2}\dfrac{x+3}{x^2+x+4}\)
b) \(\lim\limits_{x\rightarrow-3}\dfrac{x^2+5x+6}{x^2+3x}\)
c) \(\lim\limits_{x\rightarrow4^-}\dfrac{2x-5}{x-4}\)
d) \(\lim\limits_{x\rightarrow+\infty}\left(-x^3+x^2-2x+1\right)\)
e) \(\lim\limits_{x\rightarrow-\infty}\dfrac{x+3}{3x-1}\)
f) \(\lim\limits_{x\rightarrow-\infty}\dfrac{\sqrt{x^2-2x+4}-x}{3x-1}\)
\(\lim\limits_{x\rightarrow+\infty}\left(\sqrt{x^2+x+1}-\sqrt[3]{2x^3+x-1}\right)\)
\(\lim\limits_{x\rightarrow+\infty}\left(\sqrt{4x^2+x+1}-2x\right)\)
\(\lim\limits_{x\rightarrow-\infty}\left(\sqrt[3]{x^3+x^2+1}+\sqrt{x^2+x+1}\right)\)
\(\lim\limits_{x\rightarrow+\infty}\left(\sqrt{x^2+x+1}-2\sqrt{x^2-x}+x\right)\)
\(\lim\limits_{x\rightarrow+\infty}x\left(\sqrt{x^2+2x}-2\sqrt{x^2+x}+x\right)\)
Câu 1:
Xác đinh k để hàm: f(x)=\(\left\{{}\begin{matrix}\frac{x^{2016}+x-2}{\sqrt{2018x+1}-\sqrt{x+2018}}\\k\end{matrix}\right.\)liên tục tại 1
Câu 2: Cho \(lim\)(x-->1) \(\frac{x^2+ax+b}{x^2-1}=\frac{1}{2}\). Tổng S= \(a^2+b^2\) bằng bao nhiêu
Câu 3: lim(x->1) \(\frac{\sqrt{x^2+x+2}-\sqrt[3]{7x+1}}{\sqrt{2}\left(x-1\right)}=\frac{a\sqrt{2}}{b}+c\) với a/b là phân số tối giản. Tính a+b+c
Tìm các giới hạn sau :
a) \(\lim\limits_{x\rightarrow-2}\dfrac{x+5}{x^2+x-3}\)
b) \(\lim\limits_{x\rightarrow3^-}\sqrt{x^2+8x+3}\)
c) \(\lim\limits_{x\rightarrow+\infty}\left(x^3+2x^2\sqrt{x}-1\right)\)
d) \(\lim\limits_{x\rightarrow-1}\dfrac{2x^3-5x-4}{\left(x+1\right)^2}\)
