2.a. Express the function below in terms of unit step function. Calculate its derivative and provide a sketch of it. b. Express the function below in terms of unit step function. Sketch its integral.

a) Graph the feasible region of the LP. Is the feasible region unbounded? b) Are any of the above constraints redundant? If so, indicate which one(s). c) Solve the problems using the graphical method. Explain your approach and solution. d) Which constraints are active in the optimal solution? e) Suppose we add the constraint x1 + x2 >= a to LP. For which values of a: Is the constraint redundant? The optimal solution found above is no longer optimal? > The problem becomes infeasible? f) Replace the objective function with the objective function 3 x_{1}+\beta x_{2}, \text { and compute the values of } \beta \text { for which the point }(0,3 / 2) \text { is optimal }

A circuit is built with three batteries (B1, B2 and B3) and three resistors (R1, R2, and R3), as

. For the function below, Sketch each of the following signals. Use MATLAB to sketch your results (like that done in the example of basic operations using in-line function). Upload both your .m file and a published version.

A signal x(t) has a Fourier Transform given by X(\omega)=\frac{5(1+j \omega)}{8-\omega^{2}+6 j \omega} Without finding x(t), find the Fourier Transform of the following: а. х(t-3) b. x(4t) C. ei1.e12x(t) d. x(-2t)

4. Determine which of the following systems is linear or non-linear. Show proof a. y(t) = 2x(t) – 5 b.·dy/dt + 4y(t) = 2x(t) C.dy/dt+2ty(t) = x(t) d.dy/dt+ 4y(t) + 1 = x(t) e.(dy/dt) + y(t) = x²(t) f. (dy/dt)² + y(t) = x(t)

4 Find and sketch the Fourier transforms for the following signals. u(t)=(1-|t|) I_{[-1,1]}(t) v(t)=\operatorname{sinc}(2 t) \operatorname{sinc}(4 t) \text {. } \text { (c) } s(t)=v(t) \cos (200 \pi t) \text {. } (d) Classify cach of the signals in (a) (c) as baseband or passband.

Find the inverse Fourier Transform of G(\omega)=\frac{10 j \omega}{(-j \omega+2)(j \omega+3)} Y(\omega)=\frac{\delta(\omega)}{(j \omega+1)(j \omega+2)}