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QUESTION

If the Fourier series is obtained for the function $f(t)$ defined
by\\ $f(t)=\left\{\begin{array}{ll}1+t,&0\leq t<2,\\ t+2,&2\leq
t<4,\end{array}\right.$ and $f(t+4)=f(t)$,\\ STATE the value of
the Fourier series at $t=2$, (you should not calculate the Fourier
series).

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ANSWER

$f(t)$ has a discontinuity at $t=2$, so Fourier series at $t=2$
converges to

$\ds\frac{1}{2}\{f(2^-)+f(2^+)\}=\frac{1}{2}\{(1+2)+(2+2)\}=\frac{7}{2}$




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