$lim_{xto 0^+}((sin(5x)+sinx)/(sqrt(1-cosx)))$

A cura di: Administrator

Limite in forma indeterminata $frac{0}{0}$

$lim_{x rightarrow 0^+} frac{sin 5x+sin x}{sqrt{1-cos x}} =lim_{x rightarrow 0^+} (frac{5cdotfrac{sin 5x}{5x}+frac{sin x}{x}}{sqrt{frac{1-cos x}{x^2}}}) =$$lim_{x rightarrow 0^+} frac{5cdot 1+1}{sqrt{frac{1}{2}}}= frac{6}{frac{1}{sqrt{2}}} = 6sqrt{2}$