Question

Por favor, URGENTE!!! me ajudem a calcular o limite dessa equação?
(anexo)

Answer 1

Resposta:

3/2

Explicação passo a passo:

$\lim_{x \to \00} \frac{1-cos3x}{xsen3x} = \lim_{x \to \00} \frac{(1-cos3x)(1+cos3x)}{xsen3x(1+cos3x)}= \lim_{x \to \00} \frac{1-cos\²3x}{xsen3x(1+cos3x)} = \lim_{x \to \00} \frac{sen\²3x}{xsen3x(1+cos3x)} = \\\\\lim_{x \to \00} \frac{sen3x}{xsen3x(1+cos3x)} = \lim_{x \to \00} \frac{sen3x}{x} . \lim_{x \to \00}\frac{1}{1+cos3x}=3 \lim_{x \to \00} \frac{sen3x}{3x} . \lim_{x \to \00} \frac{1}{1+cos3x}=\\\\3.1.\frac{1}{1+cos3.0} =\frac{3}{1+cos0} =\frac{3}{1+1} =\frac{3}{2}$