Calculate a = x+y, b = z + 1, then keep numbers a and b. Questions marked with *** are to be graded. 1. Use the initial and final value theorems to determine x(0*) and x(oo) for the following transforms: a(s+2) *** a) X(s)= s(s+b) 2(s+2) b) X(s)= s(s+a)(s+b) 2. Obtain the inverse Laplace transform for the following transforms. a) F(s)= as+b b) F(s)= 5s+2 (s+a)(s+b)² 3. Obtain the solution x(t) of the the following differential equations: a) x+ax=0, x(0)=b, x(0) = 0 b) 2x+2x+x=a, x(0)=0, x(0)=b 4. Obtain the inverse transform of the following. If the denominator of the transform has complex roots, express x(t) in terms of sin() and cos(). *** a) X(s)= b) X(s)= 4s+a +8s+b s³+as+6 s(s+b) 5. Determine the unit-step response, f (t) = u(t) of the following models. Take zero initial conditions. a) ax+20x+bx = f(t) b) x+ax+bx=3f(t)+2f(t)

Q/ calculate the Fourier series of f(x) on the given interval f(x) = x Sin X 9 -

Q 2/ Calculate the Fourier series of f(x) on the given interval f(x) = x Sin X - 16 x ≤ メ