16. Using the contour in Figure 14.22 show that o0- 16. Using the contour in Figure 14.22 show that o0-
1.34. Draw the path parametrized by r) Cos(t)cos(t)+i sin(t ) sin(t 0sIS2 1.31. Show that the union of two regions with nonempty intersection is itself a region 1.34. Draw the path parametrized by r) Cos(t)cos(t)+i sin(t ) sin(t 0sIS2 1.31. Show that the union of two regions with nonempty intersection is itself a region
3. Use Fourier Transforms to solve u(0, )sin(ar) -o0 o0, t > 0, 3. Use Fourier Transforms to solve u(0, )sin(ar) -o0 o0, t > 0,
(a) State the First Comparison Test and show that the following series con- verges: O0 1 + cos ((2n +1)!) (b) Determine whether the following series converges (c) State the Integral Test and sketch its proof (d) Prove or disprove: If a series Σ001 an converges then Σηι an converges absolutely. e) Answer the following two questions without proof: For which r E R is the geometric series 0O convergent? What is the limit of the series in case of...
pls show all work thanks 4. If the signal X(t) = cos(0) + cos(26) + cos (46) is the input to an LTI system whose impulse response is n(t) sinc(30) sincet), what will be the output signal y() in response to this input?
o0 [26] Show that In | si =-In 2-Σ cosme for x ¢ 2aZ.
Please show work. Choose the correct general solution of the with r(t) = { a, cos (nt), [w] + 1, 2, ..,N. y= mnozcos (nt) y = c cos (@f) + C2 sin (m) y = c cos (@t) + C2 sin (61) + imz " cos (nt) T y = c cos (t) + c2 sin (ot) + Ime cos (nt) y = cj cos (ot) + C2 sin (01) + " ,cos (nt)
Show that a 20-gon is constructible using a compass and straight-edge (cos(5t) in terms if cos(t) polynomial?
Problem 10. Find the solution in the form of Fourier integrals: o0,t > 0, Зидх 0, -oo u(x, t) bounded t > 0, 0, as [0, т]), sin x хе u(x, 0) 0 х<0 or х> п. Problem 10. Find the solution in the form of Fourier integrals: o0,t > 0, Зидх 0, -oo u(x, t) bounded t > 0, 0, as [0, т]), sin x хе u(x, 0) 0 х п.
1. Show that if x(t) is an even function of t, then X(jw)2 (t) cos(wt) dt and if r(t) is an odd function of t, then X(jw)2j (t) sin(wt) dt