Question

Lim tg(hax)/x com x ->0

Answer 1

Muito bem.

Vamos aplicar a regra de L'Hospital para resolver o problema:

$\displaystyle \lim_{x \to 0}\dfrac{tgh(ax)}{x} =\displaystyle \lim_{x \to 0}\dfrac{a\cdot sech^2(ax)}{1}=\displaystyle \lim_{x \to 0}\dfrac{a}{cosh(ax)}\\ \\ \\ = \dfrac{a}{cosh^2(0)}=\dfrac{a}{1}=a\\ \\ \\ \boxed{\displaystyle \lim_{x \to 0}\dfrac{tgh(ax)}{x}=a}$