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calculo1:rolle [2022/05/31 20:09] – external edit 127.0.0.1calculo1:rolle [2022/05/31 20:11] (current) – external edit 127.0.0.1
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 Basta considerar $f(x) = \frac{1}{1+x}$ no intervalo $(-1, \infty).$ Observe que $f^{'}(x) = -\frac{1}{(1+x)^2}$ e para $x > 0$ podemos ver que $|f^{'}(x)| < 1.$  Basta considerar $f(x) = \frac{1}{1+x}$ no intervalo $(-1, \infty).$ Observe que $f^{'}(x) = -\frac{1}{(1+x)^2}$ e para $x > 0$ podemos ver que $|f^{'}(x)| < 1.$ 
 +
 +<WRAP  round tip 60%>
 +Exercício: Mostre que oara $0 < x < \pi/2$ vale:
 +  * $cos(x) > 1 - \frac{x^2}{2}$
 +  * $sen(x) > x - \frac{x^3}{6}.$
 +</WRAP>
 +
calculo1/rolle.1654038572.txt.gz · Last modified: 2022/05/31 20:09 by 127.0.0.1