Suppose further that curl, F = 9 on the shaded region D, determine the following integral: f F. dr = [5x go X

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Q: Compute the volume of D = {(x, y, z): x² + y² < z < 2y, x² + (y - 1)² < 1}.

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Q: (b) Let f:(R\{1}) → (R\{1}) and ƒ˜¹:(R\{1} ) → (R \{1}) be both defined by f(x) = f¯¹(x) = = x+1…

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Q: In Exercises 7-12, find the line integrals of F from (0, 0, 0) to (1, 1, 1) over each of the…

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Q: 4) Find the derivative of y = x²cot-¹(3x).

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Q: Using the Chinese Remainder Theorem Solve the following: Here is the theorem first: Chinese…

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Q: Find the general antiderivative of h(x) = 13x7√x. Use C for the arbitrary constant. (If necessary,…

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A: To sketch the region,  y=x+1, y=0, x=0, x=5 .

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Q: 10. Derive CRE in polar coordinates Ur = r-100 uo =-ror Using x = r cos 0 and y = r sine and chain…

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Q: 2) Use y = ax to solve 2'y" - xy' + (x+1)y=0.

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Q: 2. Show that all the roots of p(z) = 825 +324 + 4z² - 3 are inside |z| < 1.

A: Show that all the roots of  pz=8z5+3z4+4z2-3 are inside z&lt;1.

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Q: Consider the set A of binary strings of length five. Examples are 00000, 01000, 10010, etc. • Let B…

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Q: The figure shows level curves of a function f(x, y). (a) Draw gradient vectors at Q and T. Is Vf(Q)…

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Q: 4. Use Rouche's theorem to count the number of zeroes for f(z) = 2²-4+3e-² on the right half plane…

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Q: 1. Use Rouche's theorem to count the number of zeroes for p(z) = 25 +22² +52 - 1 in 2 < 1.

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Q: Question 2. Let Bt be the open ball in R" centered at ro with radius T-t (0 <t<T). Suppose f(t, x)…

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