Giới hạn nào sau đây tồn tại:

A, \(lim_{x\rightarrow+\infty}sin2x\) B, \(lim_{x\rightarrow+\infty}cos3x\) C, \(lim_{x\rightarrow0}sin\frac{1}{2x}\) D, \(lim_{x\rightarrow1}sin\frac{1}{2x}\)

Tìm các giới hạn sau:

a) \(lim_{x\rightarrow0}\dfrac{tan3x}{sin5x}\)

b) \(lim_{x\rightarrow0}\dfrac{cos2x-1}{sin^23x}\)

c) \(lim_{x\rightarrow1}\dfrac{x^2-4x+3}{sin\left(x-1\right)}\)

\(lim_{x\rightarrow0}xcos\frac{1}{x}\)

 \(lim_{x\rightarrow0}\frac{\left(1+3x\right)^3+\left(1-4x\right)^4}{x}\)

\(\sqrt{3}\sin^2\left(x\right)+\frac{1}{2}\sin2x=\tan2x\)\(\text{​​}\sqrt{3}\sin^2\left(x\right)+\frac{1}{2}\sin2x=\tan2x\)

\(D=lim_{x\rightarrow0}\frac{\left(1+2x\right)^2\left(1+3x\right)^3-1}{x}\)

Xác định \(lim_{x\rightarrow0}\frac{\left|x\right|}{x^2}\)

\(lim_{x\rightarrow0}\dfrac{\sqrt{x^3+1}-1}{x^2+x}\)

\(\lim_{x\rightarrow0}\frac{\left|x\right|}{x}\)

giúp vs nhé