The arclength of the curve r(t) = (2 cos(at/2), 2 sin"(at/2),1), between the points r =...
If you have trouble viewing the image (equations) below, they can be viewed in the attachment. The arclength of the curve r(t) = (2 cos°(t/2), 2 sin(**/2), 1). between the points r = (2,0,1) and r= (0,2,1), is given by the expression ai . 0:37 sin(ant/2) cos(asat/2) dt - f. Fill in the blank for (i, i = 1,...,6. Answers should be integers, no spaces, no punctu- ation, the only non-numeric symbol allowed is a minus sign. where 21, 22,...
Calculate the Fourier Series coefficients of x(t) = cos(2*pi*1*t) + 2*sin(2*pi*4*t). Based on your results which set of FS coefficients corresponding to the positive side of the spectra is correct. a0=0, a1=1/2, a2=1/j, a3 = 0 a1=1, a2=2, a3 = 0 a1=1/2j, a2=1/2, a3 = 0 a1=1/2, a2=2/2j, a3 = 0
2. A dragon is flying around in a pattern given by the parametric curve r(t) (cos(t) cos((sin(t) sin(t) cos(t)j. cos(t) - cos sin(t)-sin(t) cos(t))j (a) Find a formula for the velocity of the dragon at time t (b) Find all the times at which the dragon's speed is zero. Explain your reasoning. c) Does the path of the dragon contain any cusps? Explain your reasoning
2. A dragon is flying around in a pattern given by the parametric curve r(t)...
(a) Let θ : R-+ R be a smooth function. Find the (signed) curvature of the curve a:R- R2 given by cos(θ(t)) dt,I α(s) sin(θ(t)) dt Use your result to give another geometric interpretation to the (signed) curva- ture and its sign? to) rindy,R-- parmetrised with unit speed suchhat y -0and kt) - s for all seR.
(a) Let θ : R-+ R be a smooth function. Find the (signed) curvature of the curve a:R- R2 given by cos(θ(t)) dt,I...
Definition 1 Denote by Lra the straight line that is perpendicular to the direction [cos(a), sin(a) and at distance r from the origin 0= (0,0). Thus (z, y) is on the line Lra if and only if r cos(a)+y sin(a) r Common choices are r E R and 0 a<. Another potential choice might be r2 0 and -T<asT. Remark 2 The line Lra is a distance r from (0,0) in the direction perpendicular to [cos(a), sin(a)] Consequently, the point...
Definition 1 Denote by Lra the straight line that is perpendicular to the direction [cos(a), sin(a) and at distance r from the origin 0= (0,0). Thus (z, y) is on the line Lra if and only if r cos(a)+y sin(a) r Common choices are r E R and 0 a<. Another potential choice might be r2 0 and -T<asT. Remark 2 The line Lra is a distance r from (0,0) in the direction perpendicular to [cos(a), sin(a)] Consequently, the point...
- A vector tangent to the parametric curve given by r (t) = <cos (4t); sin (4t); e^(t^2)> at the point (0; 1; e^((pi/8)^2)) is a) (0; 1; e^((pi/8)^2)) b) (0; 4; e^((pi/8)^2)) c) (4; 0; e^((pi/8)^2)) d) (4; 4; e^((pi/8)^2)) e) None of the above - The curve c (t) = (cost, sint ,t) lies on which of the following surfaces: (a) cone (b) cylinder (c) sphere (d) plane (e) none of the above
Question 11 1p Determine the length of the curve r(t) = (2, 3 sin(2t), 3 cos(2t)) on the interval ( <t<27 47107 Озубл 47 0 250 √107 None of the above or below Previous Ne
find T,N,B curvature and torsion as a function of t for the space curve r(t)=sin t i+√2 cos t j+sin t k and find equation of normal and osculating planes
8.23 why ic(0+)=45mA not 50mA?
8.21 Assume the underdamped voltage response of the ocircuit in Fig. 8.1 is written as mit wv(t)= (A1 +A2)e cos wt +j(A - A2)e a sin wt en in moves -at -at 0. The initial value of the inductor current is Io, and the initial value of the capacitor voltage is Vo- Show that A2 is the conjugate of A1. (Hint: Use the same process as and A2.) outlined in the chapter to find A...