\(=\lim\limits_{x\rightarrow0}\frac{-2sin\frac{4037x}{2}.sin\frac{x}{2}}{x}=\lim\limits_{x\rightarrow0}\left(-sin\frac{4037x}{2}.\frac{sin\frac{x}{2}}{\frac{x}{2}}\right)=0.1=0\)
Mẫu là \(x^2\) thì có vẻ đẹp hơn :)
Tính các giới hạn sau:\(M=\lim\limits_{x\rightarrow0}\dfrac{\sqrt{1+4x}-\sqrt[3]{1+6x}}{1-cos3x}\)
\(N=\lim\limits_{X\rightarrow0}\dfrac{\sqrt[m]{1+ax}-\sqrt[n]{1+bx}}{\sqrt{1+x}-1}\)
\(V=\lim\limits_{x\rightarrow0}\dfrac{\left(1+mx\right)^n-\left(1+nx\right)^m}{\sqrt{1+2x}-\sqrt[3]{1+3x}}\)
Tính các giới hạn sau:
1. \(\lim\limits_{x\rightarrow a}\dfrac{x^2-\left(a+1\right)x+a}{x^3-a^3}\)
2. \(\lim\limits_{x\rightarrow1}\left(\dfrac{1}{1-x}-\dfrac{3}{1-x^3}\right)\)
3. \(\lim\limits_{h\rightarrow0}\dfrac{\left(x+h\right)^3-x^3}{h}\)
Tìm các giới hạn sau:
a) \(\lim\limits_{h\rightarrow0}\dfrac{2\left(x+h\right)^3-2x^3}{h}\)
b) \(\lim\limits_{x\rightarrow1}\dfrac{\left(x+x^2+...+x^{2021}\right)-2021}{x-1}\)
Tính các giới hạn sau:\(I_1=\lim\limits_{x\rightarrow1}\dfrac{\left(1-\sqrt{x}\right)\left(1-\sqrt[3]{x}\right)....\left(1-\sqrt[n]{x}\right)}{\left(1-x\right)^{n-1}}\)
\(I_2=\lim\limits_{x\rightarrow0}\dfrac{\left(\sqrt{1+x^2}+x\right)^n-\left(\sqrt{1+x^2}-x\right)^n}{x}\)
Tính các giới hạn sau :
a) \(\lim\limits_{x\rightarrow-3}\dfrac{x+3}{x^2+2x-3}\)
b) \(\lim\limits_{x\rightarrow0}\dfrac{\left(1+x\right)^3-1}{x}\)
c) \(\lim\limits_{x\rightarrow+\infty}\dfrac{x-1}{x^2-1}\)
d) \(\lim\limits_{x\rightarrow5}\dfrac{x-5}{\sqrt{x}-\sqrt{5}}\)
e) \(\lim\limits_{x\rightarrow+\infty}\dfrac{x-5}{\sqrt{x}+\sqrt{5}}\)
f) \(\lim\limits_{x\rightarrow-2}\dfrac{\sqrt{x^2+5}-3}{x+2}\)
g) \(\lim\limits_{x\rightarrow1}\dfrac{\sqrt{x}-1}{\sqrt{x+3}-2}\)
h) \(\lim\limits_{x\rightarrow+\infty}\dfrac{1-2x+3x^3}{x^3-9}\)
i) \(\lim\limits_{x\rightarrow0}\dfrac{1}{x^2}\left(\dfrac{1}{x^2+1}-1\right)\)
j) \(\lim\limits_{x\rightarrow-\infty}\dfrac{\left(x^2-1\right)\left(1-2x\right)^5}{x^7+x+3}\)
Tính giới hạn hàm số :
\(\lim\limits_{x\rightarrow0}\frac{e^x-e^{-x}}{\sin x}\)
Tính các giới hạn sau:
a) \(\lim\limits_{x\rightarrow1^+}\dfrac{x^3+x+1}{x-1}\)
b) \(\lim\limits_{x\rightarrow-1^+}\dfrac{3x+2}{x+1}\)
c) \(\lim\limits_{x\rightarrow2^-}\dfrac{x-15}{x-2}\)
\(\lim\limits_{x\rightarrow3}\dfrac{\sqrt{2x+3}-x}{x^2-4x+3}\)
\(\lim\limits_{x\rightarrow0}\dfrac{\sqrt[3]{x+1}-1}{\sqrt[4]{2x+1}-1}\)
\(\lim\limits_{x\rightarrow0}\dfrac{\sqrt{1+4x}-\sqrt[3]{1+6x}}{x^2}\)
Cho biết \(\lim\limits_{x\rightarrow0}\dfrac{sinax}{ax}=1\left(a\ne0\right)\). Tìm \(\lim\limits_{x\rightarrow0}\dfrac{1-cos2017x}{x^2}\)
