Question

07) Qual o maior valor que f(x) 5+5sen(5x+5) assume?

08) (FUVEST) A figura abaixo mostra parte do gráfico da função
a) sen(x)
b) 2- sen (x/2)
c) sen (x/2)
d) 2sen(x)
e) sen(2x)

Answer 1

$\Large\boxed{\begin{array}{l}\rm 7)\\\sf f(x)=5+5sen(5x+5)\\\sf Im=[5-5,5+5]=[0,10]\\\sf o~maior~valor~que~ f(x)~assume~\acute e~10.\end{array}}$$\Large\boxed{\begin{array}{l}\rm 8)\\\sf Im=[-2,2],p=4\pi\\+\underline{\begin{cases}\sf a-\diagdown\!\!\!\!b=-2\\\sf a+\diagdown\!\!\!\!b=2\end{cases}}\\\sf 2a=0\\\sf a=0\\\sf a+b=2\\\sf 0+b=2\\\sf b=2\\\sf p=\dfrac{2\pi}{c}\\\\\sf\dfrac{2\pi}{c}=4\pi\\\\\sf\dfrac{c}{2\pi}=\dfrac{1}{4\pi}\\\\\sf c=\dfrac{2\diagup\!\!\!\!\!\pi\div2}{4\diagup\!\!\!\!\!\pi\div2}=\dfrac{1}{2}\\\sf f(x)=2sen\bigg(\dfrac{x}{2}\bigg)\\\huge\boxed{\boxed{\boxed{\boxed{\sf\maltese~alternativa~b}}}}\end{array}}$