Find the complex Fourier series of the following function. f(t) = {t (π,-π

Q: Find dy. y=x√√5x+4 O 15x + 8 2√√5x+4 15x-S √√√5x+4 O 15x-8 ₂√√√5x+4 15x + 8 √√5x+4 dx dx dx

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Q: Is ? Is ? 78 -98 in the column space of - 96 78 -98 in the null space of - 96 10 1 6-9 2 10 - 23 15…

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Q: Find T, N, and k for the space curve r(t) = (10 sin t) i + (10 cos t) j+24t k.

A: Solution :-

Q: Use the divergence theorem to calculate the flux of the vector field F(x, y, z) = x³i + y³j + z³k…

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Q: 5. Please compute the mean shift vector of the figure below. The circle center is at the origin (0,…

A: Solution :   Given : Mean shift vector = 1nx∑i = 1nxxi - x   To calculate : The mean shit vector for…

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Q: Use row reduction to find the inverse of the given matrix if it exists, and check your answer by…

A: The given matrix is: 4-1-164 We have to find the inverse of the given matrix using row reduction if…

Q: The total cost in dollars of producing x lawn mowers is given by C(x) = 4,000 + 90x - x^2/3. Find…

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Q: Compute the flux of F = xi+yj+zk through the curved surface of the cylinder x² + y² = 1 bounded…

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Q: Find the solutiont of each of these recurrence relations with the given initial conditions. Use an…

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Q: Prove that any normal subgroup of G of size 2 is in the center of G. That is, For every subgroup HG…

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Q: Prove that Serret-Frenet formulae can be written in the from t' = dxt, n'=dxn, b' = d x b and…

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Q: Find f(x). f(x) = In x3 - 8ex + 2x2 03-8ex + 4x N 0 3-sex-2x 3 - 8xex-1 + 4x O 3 8ex + 4

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Q: Diagonalize the following matrix. 8-50 5 0 41-2 0 0 03 0 00 3 Select the correct choice below and,…

A: Let given matrix is ,       A = 8-5 0  50   4 1-20   0 3   00   0 0   3  Matrix  A is said to be…

Q: Exercise 5.8.2 Let B = in R². Find CB(x). {[+][6][+])} 0 be a basis of R³ and let x = 5 -1 4 be a…

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Q: Given a graph B whose vertices have degree at most 3, show that you need at least 4 colors to color…

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Q: Use the divergence theorem to calculate the flux of the vector field F(x, y, z) = x¹ỉ + (5y − 4x³y)j…

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Q: Proposition 12.5.14. Polynomials in R[x] have both right distributivity across addition: (g(x)…

A: Given: Polynomials in Rx have the both right distributivity across addition: qx+rxpx=qxpx+rxpx, and…

Q: Consider the following. [1] [33] (a) Verify that A is diagonalizable by computing P-¹AP. A = p-¹AP =…

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Q: Suppose Y = 6x-8, where x is a random variable with mean 2 and a variance of 4/3. Determine the…

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Q: Given that 0. Σ n=0 x = 1 1 x to x = n=0 x" with convergence in (-1, 1), find the power series for…

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Q: 7. For the graph shown right: a) Does it have an Euler circuit starting and ending at vertex A? If…

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Q: May i please request a hand written solution

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Q: Differentiate. Find ele ele ele ele ele AP O AP O for y=x-1 Whatsa AP O 2x³ - 3x² (x −12 - 2x3+3x2…

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Q: Evaluate 1118x B 8xyzdV, B=[2, 3]x[1,2]x[0, 1].

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Q: Exercise 7.2.7 Suppose A is an nxn matrix and let V be an eigenvector such that AV = V. Also suppose…

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Q: Use the definite integral to find the area between the x-axis and f(x) over the indicated interval.…

A: Given that f(x)=4ex-2[a, b]=[-4, 3]   The Formula for finding Area between the curve and x-axis.…

Q: 5) Consider the parallelogram with vertices (0,0), (4,0), (6,2) & (2, 2). We know the area of this…

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Q: Consider the area bound by the function f(x)=xln(x) and the x-axis over the interval from [1,2]. A.…

A: Given: Area bounded by fx=xlnx and x-axis over the interval 1,2. To find: Volume integral…

Q: 2. Find the work done by the force field F(x, y) = yi + xy j of a particle moves from (1, 0) to (-1,…

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Q: Prove the following for any given sets A, B, C and D. ACB if and only if AUB=B

A: The given problem is to prove that for the given sets A,B,C,D. A subset B if and only if A U B= B.

Q: A) Find the contour integral z²dz when C is a parabolic part y = O(0;0) to point P(1;2) P(1, 2)…

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Q: Let P(Z) = 0.42, P(Y) = 0.39, and P(ZnY) = 0.16. Use a Venn diagram to find (a) P (Z'nY'), (b)…

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Q: ..D .20 Show that fe conversion to polar coordinates. dx = √n by considering e-(x²+y²) dxdy and a

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Q: True or False. The function y = f(x) has the property that the slope always increases as increases.…

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Q: Solve the system of linear equations with the given initial conditions. x' (t) - [²1] x x(t) with…

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Q: = Determine the vector that represents a vertical shear of X k = 6. [13] in the plane with a factor…

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Q: The drug concentration in the bloodstream t hours after injection is given approximately by C(t) =…

A: Given that The Drug concentration in the bloodstream t hours after injection is given approximately…

Q: For the given differential equation write a particular solution with unde- termined coefficients. Do…

A: Since you hve posted mutiple questions, we will solve the first question for you. If you want any…

Q: Solve the following initial value problem. y" + 7y' +12y = 864x², y(0) = 17, y'(0) = -3 y(x) = =

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Q: Consider the initial value problem Suppose we know that α= B = 3t ÿ' " = [2 4 31] [2t + a 3t² +B] is…

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Q: Use the method of cylindrical shells to find the volume of the solid obtained by rotating the region…

A: Given: There is the region bounded by the curve xy = 2, x = 0, y = 2, and y = 4. To find: Our aim is…

Q: 8. Let V be the solid bounded z = 4 - x² - 4y² in the first quadrant. Draw. Let f(x) be a density…

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Q: 7. What is the last digit of 8¹00?

A: We have to find the last digit of 8^(100)

Q: •ff₂x (V x F). ds where F(x, y, z) = -7yzi+7xzj+5(x² + y²) zk and S is the part of the paraboloid z…

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Q: Show that the equation of a circle passing through the origin and having intercepts a and b on real…

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Q: 9. Given the following triple integral, draw the region of integration and rewrite the integral by…

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Q: 31)SE y²z² dV, where E is bounded by the paraboloid x = 1 - y² - z² and the plane x = 0

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Q: Consider the following matrix: 3 6 3 A-3 -6 -2 -3 -6 0 For each of the following vectors, determine…

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