Let a vector field given by V=V x W where W is an arbitrary vector field. O is always potential O V is never potential. OV has its divergence always strictly negative. OV has its divergence zero. O V has its divergence always strictly positive.

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Q: 2. Assume that Σak <∞, prove that are converges uniformly on [-1,1].

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Q: Exercise 10.4.2 Let B = in R². Find [x]B. -1 MGA 0 2 be a basis of R3 and let x = 41 -1 be a vector

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A: For polar coordinates, put .

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Q: Min Z = 12X1 + 18X2 + 8X3  5X1 + 8X2 +9X2 >= 18  9X1 + 15X2 + 12X3 >= 36  10X1 + 15X2 + 12X3 >= 45…

A: Note:  In the first constrain  is given which is corrected to

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A: 3. Let the function ƒ be defined byf(x) = cosh(x)for -  &lt; x &lt;  and satisfyf(x + 2) = f(x) .(a)…

Q: 4. Solve the Laplace equation on a disk of radius r. with boundary condition given by U(r.,0) =…

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Q: Using the method you described, what are the equilibrium points when m=85 and g=9.8? Please show…

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Q: 7 → V by a(f)(x) = x² ƒ"(x), where ƒ" (x) is the double differential of a polynomial f(x). pjection?…

A: Definition used.

Q: Consider the following function. (If an answer does not exist, enter DNE.) f(x) = x³ - 27x + 7 (a)…

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Q: Calculate the adjugate Adj(A) of the matrix A= 2 Select one: O 2 1 2 301 4 2 1 3 1 2 1 2 4 4 3 1…

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Q: (d) For the set B = {[4], [8]} ≤ Z12 determine the set V = h(B). Then for the set VC Z18 determine…

A: We use basic techniques of modular arithmetic to solve this problem.

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Q: Use Laplace transforms to solve the integral equation ...... ..... y(t) = 31² - e²² - fy(T)e y…

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