Calcular limite
07 nov 2013, 00:04
Olá, podem me ajudar ?
Utilize a Regra de L'Hôpital para calcular o seguinte limite:
Utilize a Regra de L'Hôpital para calcular o seguinte limite:
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Re: Calcular limite [resolvida]
07 nov 2013, 00:26
\(\\\\\ \lim_{x \rightarrow +\infty} \frac{e^{3x}}{x^{2}}\)
\(\\\\\\ \text{Vamos agora derivar o numerador e depois o denominador:}\)
\(\\\\\\ \lim_{x \rightarrow +\infty} \frac{3*e^{3x}}{2x}\)
\(\\\\\\\\ \frac{3}{2}*\lim_{x \rightarrow +\infty} \frac{e^{3x}}{x}\)
\(\\\\\\\\ \text{Vamos derivar novamente:} \\\\\\\)
\(\\\\\\ \frac{3}{2}*\lim_{x \rightarrow +\infty} \frac{3*e^{3x}}{1}\)
\(\\\\\ \frac{3}{2}*(+\infty)=+\infty\)
\(\\\\\\ \text{Vamos agora derivar o numerador e depois o denominador:}\)
\(\\\\\\ \lim_{x \rightarrow +\infty} \frac{3*e^{3x}}{2x}\)
\(\\\\\\\\ \frac{3}{2}*\lim_{x \rightarrow +\infty} \frac{e^{3x}}{x}\)
\(\\\\\\\\ \text{Vamos derivar novamente:} \\\\\\\)
\(\\\\\\ \frac{3}{2}*\lim_{x \rightarrow +\infty} \frac{3*e^{3x}}{1}\)
\(\\\\\ \frac{3}{2}*(+\infty)=+\infty\)