properties of periodic function
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If $f$ is a continuous periodic function of period $2π$, then is there a point c such that $f(c+π/2)=f(c)$ and a point x such that $f(x+π/4)=f(x)$? domain of $f$ is $mathbb{R}$ and $f$ is real valued.
real-analysis
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add a comment |
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If $f$ is a continuous periodic function of period $2π$, then is there a point c such that $f(c+π/2)=f(c)$ and a point x such that $f(x+π/4)=f(x)$? domain of $f$ is $mathbb{R}$ and $f$ is real valued.
real-analysis
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$g(x)= f(x)-f(x+pi/2)$ is $2pi$-periodic and continuous. If it is strictly positive then so is $sum_{n=0}^3 g(x+npi/2) =...$
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– reuns
Jan 20 at 6:39
add a comment |
$begingroup$
If $f$ is a continuous periodic function of period $2π$, then is there a point c such that $f(c+π/2)=f(c)$ and a point x such that $f(x+π/4)=f(x)$? domain of $f$ is $mathbb{R}$ and $f$ is real valued.
real-analysis
$endgroup$
If $f$ is a continuous periodic function of period $2π$, then is there a point c such that $f(c+π/2)=f(c)$ and a point x such that $f(x+π/4)=f(x)$? domain of $f$ is $mathbb{R}$ and $f$ is real valued.
real-analysis
real-analysis
edited Jan 20 at 5:51
Macrophage
1,191115
1,191115
asked Jan 20 at 5:31
jjjjjj
1094
1094
$begingroup$
$g(x)= f(x)-f(x+pi/2)$ is $2pi$-periodic and continuous. If it is strictly positive then so is $sum_{n=0}^3 g(x+npi/2) =...$
$endgroup$
– reuns
Jan 20 at 6:39
add a comment |
$begingroup$
$g(x)= f(x)-f(x+pi/2)$ is $2pi$-periodic and continuous. If it is strictly positive then so is $sum_{n=0}^3 g(x+npi/2) =...$
$endgroup$
– reuns
Jan 20 at 6:39
$begingroup$
$g(x)= f(x)-f(x+pi/2)$ is $2pi$-periodic and continuous. If it is strictly positive then so is $sum_{n=0}^3 g(x+npi/2) =...$
$endgroup$
– reuns
Jan 20 at 6:39
$begingroup$
$g(x)= f(x)-f(x+pi/2)$ is $2pi$-periodic and continuous. If it is strictly positive then so is $sum_{n=0}^3 g(x+npi/2) =...$
$endgroup$
– reuns
Jan 20 at 6:39
add a comment |
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$begingroup$
$g(x)= f(x)-f(x+pi/2)$ is $2pi$-periodic and continuous. If it is strictly positive then so is $sum_{n=0}^3 g(x+npi/2) =...$
$endgroup$
– reuns
Jan 20 at 6:39