Which one of the following options is the correct Fourier series of the periodic function $f(x)$ described below:

$$ f(x)=\left\{\begin{array}{cl} 0 & \text { if }-2 < x < -1 \\ 2 k & \text { if }-1 < x < 1 \text {; period }=4 \\ 0 & \text { if }-1 < x < 2 \end{array}\right. $$

The Fourier cosine series of a function is given by :

$$f(x) = \sum\limits_{n = 0}^\infty {{f_n}\cos nx} $$

For f(x) = cos⁴x, the numerical value of (f₄ + f₅) is _________. (round off to three decimal places)

Given two continuous time signals $$x\left( t \right) = {e^{ - t}}$$ and $$y\left( t \right) = {e^{ - 2t}}$$ which exists for $$t>0$$ then the convolution $$z\left( t \right) = x\left( t \right) * y\left( t \right)$$ is ____________.

Laplace transform of $$f\left( x \right) = \cos \,h\left( {ax} \right)$$ is