List of top Engineering Mathematics Questions on Fourier series asked in TS PGECET

If \[ f(x,y,z,w)=x^{2}e^{2y+3z}\cos(4w), \] then \[ \frac{\partial f}{\partial z} \] at $(2,0,-2,1)$ 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:

If \[ f(x,y,z,w)=x^{2}e^{2y+3z}\cos(4w), \] then \[ \frac{\partial f}{\partial z} \] at $(2,0,-2,1)$ is

The evaluation of the double integral $ \int_{-a}^{a} \int_{0}^{x} \frac{e^y}{(1+e^y)^2} \, dy \, dx $ is:

If $ u = f(r) $, $ r^2 = x^2 + y^2 + z^2 $, then \[ \frac{\partial^2 u}{\partial x^2} + \frac{\partial^2 u}{\partial y^2} + \frac{\partial^2 u}{\partial z^2} = ? \]

If for a progression, sum of the first $n$ terms is $2n^2+5n+6$ and $T_n$ is the $n^{th}$ term of the progression, then $\sum_{k=1}^{10} T_{3k} = $?

Let $f(x) = \begin{cases} h(x), & 0<x<C \\-h(-x), & -C<x<0 \end{cases}$ and $f(x+2C)=f(x) \; \forall x \in \mathbb{R}$. If the Fourier series of $f(x) = \sum_{n=0}^\infty \left(a_n \cos\frac{n\pi x}{C} + b_n \sin\frac{n\pi x}{C}\right)$ then $\sum_{n=0}^\infty a_n b_n =$

Let \[ f(x) = \begin{cases} 1 + \dfrac{2x}{\pi}, & -\pi \le x \le 0
1 - \dfrac{2x}{\pi}, & 0<x \le \pi \end{cases} \] The constant term of the Fourier series of $f(x)$ is:

If $f(x) = \begin{cases} -\pi, & \text{in } -\pi<x<0 \\ x, & \text{in } 0<x<\pi \end{cases}$ then the constant term of the Fourier series is

If \[ f(x) = \begin{cases} -\pi, & -\pi<x<0 \\ x, & 0<x<\pi \end{cases} \] then the constant term of the Fourier series is