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Consider the signal 2, defined for allt e Ras sin(at) 1<t<4 (t) 0 otherwise. Define the...
Define x1 (t) = cos(Ft) for allt € R. Define 0<t<1 Compute (11 * x2)(t), showing all your workings. 0 otherwise. 1 C ={ :
Consider a signal x(t) which is given as 1 x(t) - 2 <t<2 2 0, otherwise a) Sketch x(t) b) Sketch 3x(t – 1) c) Sketch – 2x(-t - 1) Identify all labels and amplitudes to get the whole score.
Question. Consider () - ( cos(t), sin(t)) for 0 +< 2. Parameterine this curve by are length. Chat
1. Suppose x(t)-1f 4<t<5 otherwise 0 Determine the absolute time duration of this signal and plot it. 2. Suppose lnlf n 2 otherwise Classify this signal as left-sided, right-sided, two-sided, or time-limited and plot it.
4. Let C be the closed curve defined by r(t) = costi + sin tj + sin 2tk for 0 <t<2n. (a) [5 pts] Show that this curve C lies on the surface S defined by z = 2.cy. (b) [20 pts] By using Stokes’ Theorem, evaluate the line integral| vi F. dr where F(x, y, z) = (y2 + cos x)i + (sin y + z2)j + xk
Consider the following. x = sin(t) y = csc(t) 0<t</2 (a) Eliminate the parameter to find a Cartesian equation of the curve. 1 y = X y
Solve fort, 0 < t < 27. 32 sin(t)cos(t) = 12 sin(t)
4. Let C be the closed curve defined by r(t) = costi + sin tj + sin 2tk for 0 <t< 27. (a) [5 pts) Show that this curve C lies on the surface S defined by z = 2xy. (b) (20 pts) By using Stokes' Theorem, evaluate the line integral F. dr с where F(x, y, z) = (y2 + cos x)i + (sin y + z2)j + xk
4. Let C be the closed curve defined by r(t) = costi + sin tj + sin 2tk for 0 <t<2n. (a) [5 pts] Show that this curve C lies on the surface S defined by z = 2.cy. F. dr (b) (20 pts] By using Stokes' Theorem, evaluate the line integral| " where F(t,y,z) = (y2 + cos z)i + (sin y+z)j + tk
Let C be the closed curve defined by r(t) = costi + sin tj + sin 2tk for 0 <t< 27. (a) (5 pts] Show that this curve C lies on the surface S defined by z = 2xy. (b) (20 pts] By using Stokes' Theorem, evaluate the line integral F. dr C where F(x, y, z) = (y2 + cos x)i + (sin y +22)j + xk