Sketch the region of integration and evaluate by changing to polar coordinates: 14 ["h For f(x) = √√/14x x² Answer: 38.48 rf(x) 1 x² + y² dy dx

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Q: The system of first order differential equations: has solution: yı(t) Y₂(t) = = [3₁ 13/12 = = -8…

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Q: Use the limit comparison test to determine whether an = (a) Choose a series an lim n→∞ bn = lim n-x…

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Q: f(t)=t, g(t) = 1

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Q: For matrix (0 -1 0, 1 0 0, 0 0 1), show that [adj(A)}^-1 = (1 / det(A))*A = adj (A^-1)

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Q: #6: Use the Laplace transform to solve the following initial value problem, y"8y'-9y= S(t-4), y(0) =…

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Q: ¹₁ 21 1. Find A¹ by the Cayley-Hamilton Theorem Given A =

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Q: • • Sketch the graph of an example of a function f that satisfies all of the given condition. f(0)…

A: By the given values we are drawing the function in step 2

Q: Q(x₁, x2, x3) = x² + x² + x² + 4x₁x2 − 2x13 subject to x1+x2+x3 = 0 and -x₁+x2+x3 = 0, Q(x, y, z) =…

A: To determine the definiteness of the quadratic forms subject to the given constraints, we can use…

Q: Let f RR be continuous. If f(c) > 0, prove there exists a neighborhood N of c : such that f(x) > 0…

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Q: WHAT IS THE ANSWER?

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Q: Find the Maclaurin series for f(x) = 1/(6-x-x2) and determine its radius of convergence. You must…

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Q: Evaluate the integral 3 √√9-x² √√9-x² ! 0 0 3 √√9-x² √√9-x² 177. 0 0 0 0 dz dy dx = dz dy dx. (Type…

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Q: Consider the topology 7 = {GCR:0 € Gor G=0} or T= on R. Is [0, 1) compact in (R, 7)? Explain why.

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Q: Solving the IVP by the method of Laplace transform ý" – 5y +6y = u3(t) – u5(t), ý(0)=1, g(0)=0.

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Q: Exercise 2. Consider the following metric defined on R by d(x, y) = inf {z-yl, 1}. 1. Is (R, d)…

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Q: In each of Problems 8 through 16, use the Laplace transform to solve the given initial value…

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Q: (a) Write the Taylor polynomial of degree 6 centered at 7 for cosx. (b) Use ≈ 3.14159 and the above…

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Q: can this be done on paper?

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Q: (a) Sn (b) Sn = (c) Sn = (d) Sn 12n n+1 n+3.(-1)" 3n-1 (-2)" n-1 2nn²2n + 1 2 sin n n² + 2

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Q: b) 4 2 SX²5T d 1 + 2x dx

A: To Evaluate:

Q: b d a C e

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Q: Formally prove that log(n!) = O(n log n).

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Q: The system of first order differential equations: has solution: y₁ (t) Y₂(t) - = Note: You must…

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Q: Find the derivative of the function. y'(x) = y = *sin(x) Jcos(x) In(3 + 5v) dv

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