Question

Помогите с математикой
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Answer 1

                 $\boxed{\ \ \lim\limits_{x \to 0}\, \dfrac{sinx}{x}=1\ \ \ \Rightarrow \ \ \ sinx\sim x\ ,\ x\to 0\ \ }$

$1)\ \ \lim\limits_{x \to 0}\, \dfrac{sinx}{3x}= \lim\limits_{x \to 0}\, \Big(\dfrac{1}{3}\cdot \dfrac{sinx}{x}\Big)=\dfrac{1}{3}\cdot 1=\dfrac{1}{3}\\\\\\2)\ \ \lim\limits_{x \to 0}\, \dfrac{sin6x}{3x}= \lim\limits_{x \to 0}\, \Big(\dfrac{6}{3}\cdot \dfrac{sin6x}{6x}\Big)=\dfrac{6}{3}\cdot 1=2\\\\\\3)\ \ \lim\limits_{x \to 0}\, \dfrac{2\, sin2x}{5x}= \lim\limits_{x \to 0}\, \Big(\dfrac{2\cdot 2}{5}\cdot \dfrac{sin2x}{2x}\Big)=\dfrac{4}{5}\cdot 1=\dfrac{4}{5}$

$4)\ \ \lim\limits_{x \to 0}\, \dfrac{5\, sin3x}{6x}= \lim\limits_{x \to 0}\, \Big(\dfrac{5}{2}\cdot \dfrac{sin3x}{3x}\Big)=\dfrac{5}{2}\cdot 1=\dfrac{5}{2}$