Question 2.1 Determine *(t)-h(1) where *(t) = te "tu(t) and h(t)=etu(t) by using the Fourier transform. (2 points) 22. Consider a LTI system for which the input x(!) and output y) are related by d'y().do(1) 487(0) 2u(). Determine the system output y(t) if the input is *(0) = reu(1). dr using the Fourier transform (3 points) 2.3 Consider a LTI system with impulse response h(t) = sin(4(1-1))/=(1-1). (5 points) 2.3.1 Determine the system output y() if the input is x(1) - cos(65+) using the Fourier transform (3 points) 2.3.2 Determine the system output y() if the input is x(t) = sin(4(1+1))/(t+1) us Fourier transform (2 points)

  Problem Statement Design, simulate, and build a 3-bit Digital-to-Analog Converter with full-scale analog voltage, V FS = 5V. Note that some terms used in this document refer to concepts and/or quantities that we do not explicitly study in 2EI4. Part of the project is for you to conduct research to learn the meaning of these concepts and/or quantities to be able to complete the design and write the report. Examples of these are the full-scale analog voltage (VFS), the gain error, the maximum differential non-linearity, etc. Design Contraints 1. You are limited to the dc supplies available from your Digilent module. 2. You are limited to op-amps, transistors, and resistors from your 2EI4 and 2CI4 kits. 3. Current drawn from the digital bit lines cannot exceed 1μA (ideally 0). 4. The bit levels are 0V (logic low) and 5V (logic high). 5. For convenience, you are allowed to treat 0V on a bit line as logic-1 and 5V as logic-0 (i.e. if your design requires the inversion of the bit lines, you don’t actually have to build the three inverters). Please provide the design circuit with proper description.

2. Assassination is a type of covert action. Do you think assassination is an acceptable action or is an action that should be forbidden, never done? Explain your answer.

v MI 7. Let (r) = for r e A := (0,0) (i) Find the pointwise limit f off (ii) Show that each f, is bounded on A but the pointwise limit f of the sequence is not bounded on A. (ii) Decide whether or not the convergence in () is uniform, prove your claim. (iv) use the e-strip to prove your claim in (iii).

A solid disk, a hoop, and a solid sphere are released at the same time at the top of an inclined ramp. Each has mass M and radius R. They all roll without slipping. In what order (fastest to slowest) do they reach the bottom of the ramp, if the moments of inertia of the disk, hoop, and sphere are ½ MR2, MR2, and 2/5 MR2? A) disk, hoop, sphere B) disk, sphere, hoop C) sphere, hoop, disk D) hoop, sphere, disk E) sphere, disk, hoop

R W R3 ww 10 12 ww R2 1 Write down the Kirchhoff Junction equation and solve it for I; in terms of 12 and 13. Write the result here: Ij = write down the Kirchhoff Loop equation for a loop that starts at the lower left corner and follows the perimeter of the circuit diagram clockwise. 0 write down the Kirchhoff Loop equation for a loop that starts at the lower left corner and touches the components 10V, Ry, 4V, and Ry O The resistors in the circuit have the following values . - R2 • Ry=60 Ry=130 Solve for all the following (some answers may be negative); 11 - Amperes 12 Amperes 13 Amperes NOTE: Forthin

3. Find the area between the curve y = 2^x andthe chord joining the points (0,1) and (2,4). 4. Find the coordinates of the centroid bounded bythe curve y = x^3 and the line x = 2.