A cura di: Administrator

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

$lim_{x rightarrow -infty} frac{x^6-sqrt{1-x^5}}{3+2sqrt{4x^{10}+x^2}} = lim_{x rightarrow -infty} frac{x^6 Big(1-frac{1}{x^6}cdotsqrt{1-x^5}Big)}{3+2sqrt{x^{10}cdotBig(4+frac{1}{x^5}Big)}} =$$lim_{x rightarrow -infty} frac{x^6cdotBig(1-sqrt{frac{1}{x^{12}}-frac{1}{x^7}}Big)}{3+2 |x^5|sqrt{4+frac{1}{x^5}}} = [ x < 0] =$$= lim_{x rightarrow -infty} frac{x^6cdot Big(1-sqrt{frac{1}{x^{12}}-frac{1}{x^7}}Big)}{-x^5cdotBig(frac{-3}{x^5}+sqrt{4+frac{1}{x^5}}Big)} = +infty$