f(x)= 2sen x + sen 2x + cos 3x
a)
[tex]f(\frac{\pi}{2})= 2sen (\frac{\pi}{2})} + sen 2.(\frac{\pi}{2}) + cos 3.(\frac{\pi}{2})= \\
\\
f(\frac{\pi}{2})= 2sen (\frac{\pi}{2})} + sen \ \pi + cos (\frac{3\pi}{2})= \\
\\
f(\frac{\pi}{2})=2.1+0+0= \\
\boxed{f(\frac{\pi}{2})=2}
[/tex]
b)
[tex]f(\pi)= 2sen \pi + sen 2 \pi + cos 3 \pi = \\
\\
f(\pi)=2.0+0+(-1)= \\
\\
\boxed{f(\pi)=-1}[/tex]
c)
[tex]f(0)= 2sen 0 + sen 2.0 + cos 3.0 \\
\\
f(0)=2.0+0+1
f(0)=1
\\
\\
f(2\pi)= 2sen 2\pi + sen 2.2\pi + cos 3.2\pi \\
\\
f(2\pi)=2.0+0+1 \\
\\
f(2\pi)=1 \\
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f(\frac{3\pi}{2})= 2sen \frac{3\pi}{2} + sen 2.\frac{3\pi}{2} + cos 3.\frac{3\pi}{2}= \\
\\
f(\frac{3\pi}{2})= 2sen \frac{3\pi}{2} + sen 3\pi + cos \frac{9\pi}{2}= \\
\\
f(\frac{3\pi}{2})=2.(-1)+0+0=-2
[/tex]
Logo
[tex]\boxed{\frac{f(0)+f(2\pi)}{f(\frac{3\pi}{2})}=\frac{1+1}{(-2)}=-1}[/tex]
