Ensino Superior ⇒ Cálculo 2 Tópico resolvido

[Wilson250]

quanto vale lim de sen(t)/t com t tendendo ao infinito

[rcompany]

[tex3]
\begin{align}
(\forall t \in\mathbb{R},\,-1\leqslant\sin t\leqslant1)&\implies (\forall t > 0,\,-\frac{1}{t}\leqslant\frac{\sin t}{t}\leqslant\frac{1}{t})\\
&\implies \lim\limits_{x\to+\infty}\frac{\sin t}{t}=0\text{ já que }\left\{\begin{array}{}\lim\limits_{x\to+\infty}-\dfrac{1}{t}=0\\\lim\limits_{x\to+\infty}\dfrac{1}{t}=0\end{array}\right.\\[24pt]
\text{Idem quando }x\longrightarrow-\infty

\end{align}
[/tex3]

Código: Selecionar tudoSHIFT+Click na eq = ZOOM

[tex3]
\begin{align}
(\forall t \in\mathbb{R},\,-1\leqslant\sin t\leqslant1)&\implies (\forall t > 0,\,-\frac{1}{t}\leqslant\frac{\sin t}{t}\leqslant\frac{1}{t})\\
&\implies \lim\limits_{x\to+\infty}\frac{\sin t}{t}=0\text{ já que }\left\{\begin{array}{}\lim\limits_{x\to+\infty}-\dfrac{1}{t}=0\\\lim\limits_{x\to+\infty}\dfrac{1}{t}=0\end{array}\right.\\[24pt]
\text{Idem quando }x\longrightarrow-\infty

\end{align}
[/tex3]