tính \(\lim\limits_{x\rightarrow0}\left(\dfrac{1-\sin x-\cos x}{1+\sin3x+\cos3x}\right)\)
Tính các giới hạn sau:
a) \(\lim\limits_{x\rightarrow0^-}\dfrac{2\left|x\right|+x}{x^2-x}\)
b) \(\lim\limits_{x\rightarrow-\infty}\left(\sqrt{x^2-x}-\sqrt{x^2-1}\right)\)
c) \(\lim\limits_{x\rightarrow-\infty}\dfrac{\sqrt[3]{1+x^4+x^6}}{\sqrt{1+x^3+x^4}}\)
Tính
\(L=\lim\limits_{x\rightarrow0}\dfrac{\left(1+2013x\right)^{2014}-\left(1-2014x\right)^{2013}}{x^2}\)
Các bạn tính giúp mình mấy câu này với:
1. \(\lim\limits_{x\rightarrow\left(-1\right)-}\dfrac{\sqrt{x^2-3x-4}}{1-x^2}\)
2. \(\lim\limits_{x\rightarrow2^+}\left(\dfrac{1}{x-2}-\dfrac{x+1}{\sqrt{x+2}-2}\right)\)
3. \(\lim\limits_{x\rightarrow+\infty}\dfrac{3x^2-5sin2x+7cos^2x}{2x^2+2}\)
4. \(\lim\limits_{x\rightarrow+\infty}\left(x.sin\left(\dfrac{1}{3x}\right)\right)\)
5. \(\lim\limits_{x\rightarrow0}\dfrac{\sqrt{2x+1}.\sqrt[3]{3x+1}.\sqrt[4]{4x+1}-1}{x}\)
6. \(\lim\limits_{x\rightarrow0}\left(\dfrac{\sqrt{9x+4}-\sqrt[3]{4x^{^2}+8}}{sinx}\right)\)
Tính
\(\lim\limits_{x\rightarrow0}\dfrac{\left(x^2+2014\right)\sqrt[2014]{1-2014x}-2014}{x}\)
Tính giới hạn: \(A=\lim\limits_{x\rightarrow0}\dfrac{\left(x^2+2017\right)\sqrt[5]{1-5x}-2017}{x}\)
Tính các giới hạn
a) \(\lim\limits_{x\rightarrow0}\dfrac{\sqrt{x+1}-\sqrt[3]{x-1}}{x}\)
b) \(\lim\limits_{x\rightarrow2}\dfrac{\sqrt[3]{x-3}+\sqrt[4]{2x-3}}{x-2}\)
\(\lim\limits_{x\rightarrow3}\dfrac{f\left(x\right)-80}{x-3}=5\). Tính \(\lim\limits_{x\rightarrow3}\dfrac{\sqrt[4]{f\left(x\right)+1}-3}{2x^2-11x+15}\)
Tính
\(\lim\limits_{x\rightarrow0}\dfrac{\sqrt[3]{x+1}.\sqrt{2022x^2+x+1}-1}{x}\)
