(3) Determine the TAYLOR'S EXPANSION of exactly one of the following expres- sions: (3.1) cosh(z) 22...
(4) Determine the TAYLOR'S EXPANSION of exactly one of the following expres- sions: (4.1) 2+1 2 +4 on 12 +11 > 3. (4.2) 9i 9i – 24 on [2< V3.
Problem 3. Given: f(t) 3 -22 f(t) 0 otherwise 3.1 Determine which one of the following expressions is the (a) (1.5jw) (ee (b) (3/jw) (e -e Fourier transform for f: jw -jw jw) (e e 1.5jw 1.5jw (d) Bjw) (e (e) (2jw) (ee) 3.2 Rewrite F(w) as as a trigonometric sinusoidal function and sketch its wavefom. 3.3 Determine the values of first two frequency terms (w1 and w2) where F(w)-0. 3.4 Determine the inverse Fourier transform of f(t) and sketch...
Consider the following complex-variable function cosh a < T f(z) la! cosh πχ, a) Find all its singularities, state their nature and compute the residues b) Consider the rectangular contour y with vertices at tR and tRi. Evaluate 6 6 dz cosh πχ c) Using the previous result take the limit R-to prove that cosh ax (10] 2 cos (g Hint: remember that cosh(a + b) -cosh a cosh b + sinh a sinh b d) Why is the above...
11. Show that following are an entire function. f(z)= e-? f(3) = cosh(z) (a) (b) 12. Find the derivative of the following using Cauchy- Reimann equations: ali d [2z - i dz z + 2i Z + 2z3 (a) (b)
(2) Determine the RADIUS and ANNULUS OF CONVERGENCE of exactly one of the following POWER SERIES: (2.1) (z – 4i)" n2 · [1 + V3i]2n n=1
3. Use partial-fraction expansion to find the inverse z-transform of the following. You need to simplify your results so that r{n] is a real signal. (a) 22 X(z) 2-1)(2-0.5)(2-2) EECS 50, Fall 2019 2 (b) X(2)2221
(6 points) Determine if the following is possible for some real number z. Explain why using a full sentence(s). (a) (2 points) cos(z) = 3.2 (b) (2 points) sec(z) = 6 (c) (2 points) cot(T) = z
Find the derivative of the following: f(x)=( Sinh(Sin-(x2)))3 оа. Select one: - 6X(Sinh(Sin-(x^))) Cosh(Sin-1(xº) √1-8" 3(Sinh(Sin-'(x2)))?Cosh(Sin-'(x2)) O b. 71-X 3(Sinh(Sin '(x2))) Cosh(Sin ?(X)) O c. 71-X 6XCosh(Sin-'(x?)) O d. V1-14
Refer to the circuit diagram depicted in Figure 1 below 10245V 20 20V (3-4021 10 22 3.1 Figure 1 Determine the Thevenin equivalent impedance of the network provided in figure 1 (Show all steps) 3.2 Calculate the open circuit voltage VAD 3.3 Draw the Thevenin equivalent circuit of the network and determine the current through a load Z=332 + 14 41 connected across AB terminals (5) [12]
1. If Ea) 2. The Fourier series expansion of the function f() which is defined over one period by , 1<zc2 is f(z) = ao + Find the coefficients an and simplify you answer. 1 z sin ax cos ar Jzcos az dz = Hint: f(x) cos(n") dz and a.-Th 3. The propagation of waves along a particular string is governed by the following bound- ary value problem u(0,t) 0 ue(8,t)0 u(x,0) = f(x) u(x,0) g(x) Use the separation of...