Question

lim x → 0 sen ax / bx
pode resolver? por favor!

Answer 1

$\lim_{x \rightarrow\ 0}\frac{sin(ax)}{bx}=\frac{1}{b} \lim_{x \rightarrow\ 0}\frac{sin(ax)a}{ax}=\frac{a}{b}\lim_{x \rightarrow\ 0}\frac{sin(ax)}{ax}$

Como o limite:

$\lim_{x \rightarrow\ 0}\frac{sin(ax)}{ax}$

é igual a 1, temos:

$\frac{a}{b}$

Answer 2

$\boxed{\begin{array}{l}\displaystyle\sf\lim_{x \to 0}\dfrac{sen(ax)}{bx}.\\\underline{\rm nultiplicando~e~dividindo~por~a~temos\!:}\\\displaystyle\sf\lim_{ x \to 0}\dfrac{sen(ax)}{bx}\cdot\dfrac{a}{a}\\\displaystyle\sf \dfrac{a}{b}\lim_{x \to 0}\dfrac{sen(ax)}{ax}\\\underline{\rm fac_{\!\!,}a} \\\sf u=ax\implies x=\dfrac{u}{a}\\\sf x \to 0~quando~u \to 0.\\\displaystyle\sf\dfrac{a}{b}\lim_{u \to 0}\dfrac{sen(u)}{u} =\dfrac{a}{b}\cdot1=\dfrac{a}{b}.\end{array}}$