Let w be the differential form rdr+ydy zdz (i) Show that w is closed. (ii) Ís w exact? If it is, find f such that df-w. If not, explain why not. Let w be the differential form rdr+ydy zdz (i) Sh...
8. Let w be the differential form yzdydz + zxdzdx + xydrdy. (i) Show that w is closed. (ii) Is w exact? If it is, find η such that dr-w. If not, explain why not.
8. Let w be the differential form yzdydz + zxdzdx + xydrdy. (i) Show that w is closed. (ii) Is w exact? If it is, find η such that dr-w. If not, explain why not.
8. Let w be the differential form yzdydz + zxdzdx + xydrdy. (i) Show that w is closed. (ii) Is w exact? If it is, find η such that dr-w. If not, explain why not.
Let UCR2 be the open annuls: Define pe N (U) be Show that p is a closed 1-form but argue that it is not an exact two form This means that dp 0 but there does not exist a function f: U - R such that df = ip. Hint: Integrate ip over suitable closed curve.
Let UCR2 be the open annuls: Define pe N (U) be Show that p is a closed 1-form but argue that it is not...
(1 point) Use the "mixed partials" check to see if the following differential equation is exact. lf It is exact find a function F(xy whose differential, dF(x y is the left hand side of the differential equation. That is, level curves F x,y) = Care solutions to the differential equation First: M, (x, y) = | 3-e^x(cosy) and N(x, y)3-enx(cosy) If the equation is not exact, enter not exact, otherwise enter in F(x,y) here (-e1xsiny+3y)+(3x-excosy)
(1 point) Use the "mixed...
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Let u=8i - 8j, and w=-i-2j. Find ||w-ul. w-ul=1 (Type an exact answer, using radicals as needed.) Let u=8i - 8j, and w=-i-2j. Find ||w-ul. ||w-ul=1 (Type an exact answer, using radicals as needed.)
solution to 2
(ii) Show that the image of f is not a subspace of R 2. Let U, V, and W be vector spaces over the field k, and let f: Ux V- W be a bilinear map. Show that the image of f is a union of subspaces of W. 3. Let k be a field, and let U, V, and W be vector spaces over k. Recall that
(ii) Show that the image of f is not...
Let u=8i - 8j, and w=-i-2j. Find ||w-ul. w-ul=1 (Type an exact answer, using radicals as needed.)
Problem I. Let f: R -> R be any map and suppose that the graph Tf CR is closed and connected. Show that f is continuous.
Problem I. Let f: R -> R be any map and suppose that the graph Tf CR is closed and connected. Show that f is continuous.
(6 points) Use repeated substitution to find an exact (non-asymptotic) closed-form ex- pression (a non-recursive function of n) for the recurrence F(n) - 12 F(n-1)+2 n2 2 Show your work, and write your final answer in the box at the bottom of the page.
(1point) Let r = xi + yj + zk and a = 4i +4j + 2k. (a) Find VG a). (b) Let C be a path from the origin to the point with position vector ro - ai+bj +ck. Find Jc VG a) df (c) If I I roll = 10, what is the maximum possible value of IV(F. , dF2 (Be sure you can explain why your answer is correct.) maximum value of Jc VG.ã di
(1point) Let r...