the answer is
why domain of p is 【0,1】in here
And the answer continuous like this , the second question is why the surface integral over the top z=2?
And how to get the surface integral over the top of the cylinder and the surface integral over the bottom of the cylinder?
The answer is why domain of p is 【0,1】in here And the answer continuous like this , the secon...
3. Under the influence of a vector field a particle spirals on the surface of a unit sphere toward the (t)-t and ф(t)- uppermost pole. With its spherical angular positions parametrically defined by 24t, the particle's path can be defined t€[3m/2.2n. r(t)-sin(θ(t)) cos(d(t)) ị t sin(θ(t)) sin(φ(t))J+cos(θ(t)) k, Compute the work done by the constant vector field F(,y,z) 1 k in moving the particle along this path We were unable to transcribe this image 3. Under the influence of a...
#1 Exercises with Vectors-II Name [1] Suppose you have two vectors, a and b, that have the same length, so that lal-lb but they point in different directions. Denote the angle between them by . Show that tan(0/2) la-bMa+b Hint: Compute the right-hand side using the fact that lal-bl, and the trig identities 1-cos θ-2sin'(9/2) and 1+cos9-2cos(θ/2) 12] Vectors in 3-dimensions are often parameterized in terms of their length and two angles, as shown in the figure (think of a...
MARK WHICH STATEMENTS BELOW ARE TRUE, USING THE FOLLOWING, Consider Vf(x, y, z) in terms of a new coordinate system, x= x(u, v, w), y=y(u, v, w), z=z(u, v, w). Let r(s) = x(s) i+y(s) + z(s) k be the position vector defining some continuous path as a function of the arc length. Similarly for the other partial derivatives in v and w. For spherical coordinates the following must also be true for any points, x = Rsin o cose,...
the excercise concerns the function (x^2 + y^2)* e^(1-x^2 - y^2) please do all parts MA330 Homework #4 1. This exercise concerns the function its gradient vector field F-vo See the plots of each below. a) Compute the partial derivatives os and ty to find the gradient field vo. (b) In MA231, learned 1, you learned that mixed second-order partial derivatives of reasonable functions Verity that here by computing day and dys and checking that they are the same. should...
2. Consider the vector field F = (yz - eyiz sinx)i + (x2 + eyiz cosz)j + (cy + eylz cos.) k. (a) Show that F is a gradient vector field by finding a function o such that F = Vº. (b) Show that F is conservative by showing for any loop C, which is a(t) for te (a, b) satisfying a(a) = a(6), ff.dr = $. 14. dr = 0. Hint: the explicit o from (a) is not needed....
(1 point) Compute the outward flux of the vector field F(:,, :) - 2ri + 4y + 4k across the boundary of the right cylinder with radius 5 with bottom edge at height z = 5 and upper edge at 2= 6. Note: The vectors in this field point outwards from the origin, so we would expect the flux across each face of the cylinder to be positive Part 1 - Using a Surface Integral First we parameterize the three...
Consider a cylindrical capacitor like that shown in Fig. 24.6. Let d = rb − ra be the spacing between the inner and outer conductors. (a) Let the radii of the two conductors be only slightly different, so that d << ra. Show that the result derived in Example 24.4 (Section 24.1) for the capacitance of a cylindrical capacitor then reduces to Eq. (24.2), the equation for the capacitance of a parallel-plate capacitor, with A being the surface area of...
Compute the following problems using Math Lab. Instructions: Answer All Questions using MATLAB commands. Question 1. Create a vector of the even whole numbers between 31 and 75. Question 2. Let x [2516] a. Add 16 to each element b. Add 3 to just the odd-index elcments c. Compute the square root of each element d. Compute the square of each element Question 3. Let x 13 268T and y [4 1 3 5] (NB. x and y should be...
NO.25 in 16.7 and NO.12 in 16.9 please. For the vector fied than the vecto and outgoing arrows. Her can use the formula for F to confirm t n rigtppors that the veciors that end near P, are shorter rs that start near p, İhus the net aow is outward near Pi, so div F(P) > 0 Pi is a source. Near Pa, on the other hand, the incoming arrows are longer than the e the net flow is inward,...