Here is a summary of the questions from the uploaded image:

Question 10:

1. (a): Find the Fourier cosine and sine integrals of $f(x) = e^{-kx}$, for $x > 0$, $k > 0$.
2. (b): Find the Fourier transform of the function $f(x)$ defined as: \begin{cases} 1 - x^2, & |x| \leq 1 \\ 0, & |x| > 1$$ and then evaluate: $$\int_0^\infty \frac{x \cos x - \sin x}{x^3} \cos\left(\frac{x}{2}\right) dx.$$

Question 11:

1. (a): Obtain the Z-transform of the sequence $\{f_n\}$, where $f_n$ is given by:
   • $f_n = a^n$,
   • $f_n = n$,
   • $f_n = n^2$.
2. (b): Using the convolution theorem, find $Z^{-1} \left\{ \frac{z^2}{(z-a)(z-b)} \right\}$.
3. (c): Solve the difference equation using Z-transforms: $y_{n+1} - 3y_n = 0, \quad y_0 = 1.$

Would you like detailed solutions for any specific part?