Show that the differential form in the integral is exact. Then evaluate the integral. (2.0.2) |...
Show that the differential form in the integral is exact. Then evaluate the integral. (0.4.4) sin y cosx dx + cos y sin x dy + 4 dz (1,0,0) s Compute the partial derivatives. ӘР ON ay dz Compute the partial derivatives. OM ap dz Compute the partial derivatives. ON OM ду Select the correct choice below and fill in any answer boxes within your choice. O A sin y cos x dx + cos y sin x dy +...
Show that the differential form in the integral is exact. Then evaluate the integral. (3,0.1) sin y cos x dx + cos y sin x dy + 8 dz (1,0,0) Compute the partial derivatives. OP ON dy dz Compute the partial derivatives. дМ OP 0 dx Compute the partial derivatives. ON OM Select the correct choice below and fill in any answer boxes within your choice. 13.0.1 sin y cos x dx + cos y sin x dy + 8...
S Show that the differential form in the integral below is exact. Then evaluate the integral. (-1,-1,-1) 4x dx + 4y dy + 6z dz (0,0,0) Select the correct choice below and fill in any answer boxes within your choice. OA (-1,-1,-1) 4x dx + 4y dy + 6z dz (0,0,0) (Simplify your answer. Type an exact answer.) OB. The differential form is not exact. S
Let F, =M, i+Nyj+Pk and F2 =Mzi + N2j+Pyk be differentiable vector fields and let a and b be arbitrary real constants. Verify the following identities. a. V. (aF7 +bF2)=aV.Fy+bV.F2 b. Vx(aF, +bF2) =aVxF, +bVxF2 c. V. (F, ⓇF_)=F2.VxF,-F7.VxFz a. Start by expressing af, +bF, in terms of My, Ng, P1, M2, Ny, and P2- V.(aF, + bFy)=v-[i+Di+(k] a a Use the definition of the divergence of a vector field, denoted div For V.F, to expand the right side of...
Please Answer the Following Questions (SHOW ALL WORK) 1. 2. 3. 4. Write an iterated integral for SSSo flexy.z)dV where D is a sphere of radius 3 centered at (0,0,0). Use the order dx dz dy. Choose the correct answer below. 3 3 3 OA. S S f(x,y,z) dx dz dy -3 -3 -3 3 OB. S 19-x2 19-32-22 s f(x,y,z) dy dz dx 19-x2 - 19-2-22 s -3 3 3 3 oc. S S [ f(x,y,z) dy dz dx...
Problem 5 (25 points) Show that the differential equation (siny -ysinx)dx + (cosx + xcosy - y)dy = 0 is exact, and hence find the general solution. Solve the following. Simplify answers as much as possible. (a) (1+y?)dx -xydy = 0 , y(5) - 2 (b) e(sinx)dy +(e X + 1 cosx)dx = 0
II. Consider the differential dz = xy dx + y'x dy (a) Compute Az in going from the point (4.4) to (8,8) along the path Constant x - ----- constant y ---> (8,8) (4,4) -> (4.8) ---- (b) Compute Az from (4,4) to (8,8) along the path y = x. (©) Use Euler's test for exactness on the differential dz = xy dx + y'x dy Is the differential exact or inexact? Are your results to parts (a) and (b)...
A. Show that the differential forms in the integrals are exact. B. Then evaluate the integrals. (0,1) (3x - y + + 1) dx + (-x - 2y + 2) dy
4. (a Let (sin( x cos( ) dr + (x cos(x + y) - 2) dy. dz= Show that dz is an exact differential and determine the corresponding function f(x,y) Hence solve the differential equation = z sin( Cos( y) 2 x cos( y) dy 10] (b) Find the solution of the differential equation d2y dy 2 y e dx dæ2 initial conditions th that satisfi 1 (0) [15] and y(0) 0 4. (a Let (sin( x cos( ) dr...
(1 point) Use the "mixed partials" check to see if the following differential equation is exact. If it is exact find a function F(x, y) whose differential, d F(x, y) is the left hand side of the differential equation. That is, level curves F(x, y) = C are solutions to the differential equation (-3e* sin(y) + 4y)dx + (4x – 3e* cos(y))dy = 0 First, if this equation has the form M(x, y)dx + N(x, y)dy = 0: My(x, y)...