Resposta:
3/2
Explicação passo a passo:
[tex]\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}[/tex]
