Question:medium
If $f(x)=e^{-x}$ in $(-1,1)$ and the Fourier series of $f(x)$ is given by
\[
f(x)=\frac{a_0}{2}+\sum_{n=1}^{\infty}(a_n\cos nx+b_n\sin nx),
\]
then the Fourier coefficient $a_0$ is:
If $f(x)=e^{-x}$ in $(-1,1)$ and the Fourier series of $f(x)$ is given by
\[
f(x)=\frac{a_0}{2}+\sum_{n=1}^{\infty}(a_n\cos nx+b_n\sin nx),
\]
then the Fourier coefficient $a_0$ is:
Show Hint
Use identities:
\[
\sinh x=\frac{e^x-e^{-x}}{2}
\]
to simplify Fourier integrals.
Updated On: Jun 29, 2026
- 1
- 0
- $2\cosh 1$
- $2\sinh 1$
Show Solution
The Correct Option is D
Solution and Explanation
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