Esercizi sui Limiti

  • Materia: Esercizi sui Limiti
  • Visto: 1261
  • Data: 08/05/2008
  • Di: Redazione StudentVille.it

$lim_{xto-infty}((x^6-sqrt(1-x^5))/(3+2sqrt(4x^10+x^2)))$

esercizio svolto o teoria

A cura di: Administrator

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

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