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2. Reparameterize each of the following paths in terms of their arclength S. a)(t)(t2, t,) b) )(sin(t), t, cos(t))...
The arclength of the curve r(t) = (2 cos(at/2), 2 sin"(at/2),1), between the points r = (2,0,1) and r = (0,2,1), is given by the expression -] . a37 sin(a4nt/2) cos(azat/2) dt = 06. 02 Fill in the blank for ai, i = 1,...,6. Answers should be integers, no spaces, no punctu- ation, the only non-numeric symbol allowed is a minus sign. where a1, 22, 23, 24, 25 and 26 are integers given by: 01 = A2 = A3 =...
How do you solve the following? Consider the curve r=(e^(-5t)cos(-t),e^(-5t)sin(-t),e^(-5t). Compute the arclength function s(t): (with initial point t=0).
(a) xi (t) =4(sin(31) + cos(3t)] (b) x2(t) = sin(41) 1.18 For each of the following functions, indicate if it exhibits even symmetry, odd symmetry, or neither one. (a) Xi (t) = 1-e-2t (b) x2(t) = 1-e-2t2 1.19 Generate plots for each of the following step-function waveforms over the time span from-5 s to +5 s. (a) xi (t)=-611 (t + 3) (b) x2(t) = 1011(1-4) (c) x3(t) = 411 (t + 2) _ 411 (1-2)
P9.3 A random process X(t) has the following member functions: x1 (t) -2 cos(t), x2(t)2 sin(t), x3(t)- 2 (cos(t) +sin(t)),x4t)cost) - sin(t), xst)sin(t) - cos(t).Each member function occurs with equal probability. (a) Find the mean function, Hx (t). (b) Find the autocorrelation function, Rx(t1,t2) (c) Is this process WSS? Is it stationary in the strict sense?
3. If T2 = r3 cos(0) sin(d) and v2 = sin(0) cos(O)f + r sin(0)θ + r2 sin(d)φ compute the following (a) ▽T, (b) ▽.
Assume sin S = {}, cos S = 4, sin T = 1, cos T = Find the given quantities without using a calculator. Give answer as a fraction (for instance on half would be written 1/2) Sin (S +T)= Cos (S+T)=
Please explain, thank you.
Show that the curve x = 5 cos t, y = 2 sin tcos t has two tangents at (0, 0) and find their equations (smaller slope) (larger slope)
Show that the curve x = 5 cos t, y = 2 sin tcos t has two tangents at (0, 0) and find their equations (smaller slope) (larger slope)
2. Determine the following: T/2 (3 sin2 t cost İ + 3 (a) j + 2 sin t cos t k) dt sin t cos" t tan2 t t3-8 (b) lim sin t sin 2t t +2
2. Determine the following: T/2 (3 sin2 t cost İ + 3 (a) j + 2 sin t cos t k) dt sin t cos" t tan2 t t3-8 (b) lim sin t sin 2t t +2
sin(s) cos(t)] Let S be the unit sphere, with the usual parameterization γ(st)-|sin(s)sin(t) cos(s) Let w zdz Λ dy. Find w.
sin(s) cos(t)] Let S be the unit sphere, with the usual parameterization γ(st)-|sin(s)sin(t) cos(s) Let w zdz Λ dy. Find w.
Define f: R2R3 b f(s,t) (sin(s) cos(t), sin(s) sin(t), cos(s)). (a) Describe and draw the image of f. (b) Proeve i.baat uts dilikur#xot.ial le. (c) Find the Jacobian matrix of f at (π/3, π/4) (d) Describe and draw the im age of Df(m/3, π/4). (e) Draw the image of Df(n/3, π/4) translated by f(n/3, π/4). (f) Describe the relationship between the image of f and the translated image of Df(T/3,/4) in nart (e
Define f: R2R3 b f(s,t) (sin(s) cos(t),...