Limite com raízes [resolvida]
30 ago 2013, 19:23
Lim √(x³+x²) - √(x³)
x→∞
a) 0
b) 1/3
c) 1/2
d) 2/3
e)∞
x→∞
a) 0
b) 1/3
c) 1/2
d) 2/3
e)∞
Re: Limite com raízes
30 ago 2013, 20:36
olá segue resolução 
.
\(\\\\ \lim_{x\rightarrow \infty } \sqrt{x^{3}+x^{2}}-\sqrt{x^{3}} \\\\ \lim_{x\rightarrow \infty } \frac{(\sqrt{x^{3}+x^{2}}-\sqrt{x^{3}})*(\sqrt{x^{3}+x^{2}}+\sqrt{x^{3}})} {\sqrt{x^{3}+x^{2}}+\sqrt{x^{3}}} \\\\ \lim_{x\rightarrow \infty }\frac{x^{2}:x^{2}}{(\sqrt{x^{3}+x^{2}}+\sqrt{x^{3}}):x^{2}} \\\\ \lim_{x\rightarrow \infty }\frac{1}{\sqrt{\frac{1}{x}+\frac{1}{x^{2}}}+\sqrt{\frac{1}{x}}} =\infty\)
.\(\\\\ \lim_{x\rightarrow \infty } \sqrt{x^{3}+x^{2}}-\sqrt{x^{3}} \\\\ \lim_{x\rightarrow \infty } \frac{(\sqrt{x^{3}+x^{2}}-\sqrt{x^{3}})*(\sqrt{x^{3}+x^{2}}+\sqrt{x^{3}})} {\sqrt{x^{3}+x^{2}}+\sqrt{x^{3}}} \\\\ \lim_{x\rightarrow \infty }\frac{x^{2}:x^{2}}{(\sqrt{x^{3}+x^{2}}+\sqrt{x^{3}}):x^{2}} \\\\ \lim_{x\rightarrow \infty }\frac{1}{\sqrt{\frac{1}{x}+\frac{1}{x^{2}}}+\sqrt{\frac{1}{x}}} =\infty\)