Resolver lim_(x→-∞){[(x+3)/2]*e^x}
21 nov 2012, 03:03
Como resolver este limite?
\(\lim_{x \to -\infty }\left ( \frac{x+3}{2}e^{x} \right )\)
\(\lim_{x \to -\infty }\left ( \frac{x+3}{2}e^{x} \right )\)
Re: Resolver lim_(x→-∞){[(x+3)/2]*e^x}
21 nov 2012, 22:12
Agora me dei conta que a solução é trivial.
\(\lim_{x \to -\infty }\left ( \frac{x+3}{2}e^{x} \right )\)
\(\rightarrow \lim_{x \to -\infty }\left ( \frac{x+3}{2e^{-x}} \right )\)
\(\rightarrow \lim_{x \to -\infty }\left ( \frac{-x-3}{2e^{-x}} \left ( -1 \right )\right )\)
Podemos agora aplicar L'Hôpital:
\(\overset{L'H}{\rightarrow} \lim_{x \to -\infty }\left ( \frac{1}{2e^{-x}}\left ( -1 \right ) \right )=0\)
\(\therefore \lim_{x \to -\infty }\left ( \frac{x+3}{2}e^{x} \right )=0\)
\(\lim_{x \to -\infty }\left ( \frac{x+3}{2}e^{x} \right )\)
\(\rightarrow \lim_{x \to -\infty }\left ( \frac{x+3}{2e^{-x}} \right )\)
\(\rightarrow \lim_{x \to -\infty }\left ( \frac{-x-3}{2e^{-x}} \left ( -1 \right )\right )\)
Podemos agora aplicar L'Hôpital:
\(\overset{L'H}{\rightarrow} \lim_{x \to -\infty }\left ( \frac{1}{2e^{-x}}\left ( -1 \right ) \right )=0\)
\(\therefore \lim_{x \to -\infty }\left ( \frac{x+3}{2}e^{x} \right )=0\)