Question

Find the value of u3 if \(U(z) = \frac{3z^2+2z+10}{(z-1)^4} \).

(a) 12

(b) 13

(c) 14

(d) 15

I have been asked this question by my school principal while I was bunking the class.

My question comes from Linear Difference Equations and Z topic in division Fourier Integral, Fourier Transforms and Integral Transforms of Engineering Mathematics

Answer 1

Right option is (c) 14

Easy explanation: Taking limz→∞ U(z), we get 0 which is u0. Now using the shifting property and again using the limit we get u1 which is 0. Again, by using the shifting property we get u2 which is 3. Now, by using shifting by 3 properties, we get the value of u3 which is 14.