Consider the polar curves C₁ : r = 2 cos 0 and C₂ : r = 2 cos 30, and let R be the shaded region as shown below. SET UP the (sum of) definite integral(s) equal to the area of R. ग 2

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A: As per our policy, we are allowed to attempt the first part of the question. kindly post remaining…

Q: 6. Let S be the surface with equation 4y² + 4z² − x² − 16 = 0 a. Find an equation of the trace of S…

A: Solution

Q: 5. D = 2000 2 1 -5 Evaluate D.

A: 2  0  0   0-5  3  0   0   3  2  4   0   4  2  1-5  =  (2)(-1)1+1 3  0   02  4   02  1-5…

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A: A=7-340-721-146010-3-5 WE HAVE TO FIND LU FACTORIZATION.

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Q: 2. Consider the polar curves C₁: r = 4 + ³² cos 0 and C₂:r = 2 - cos as shown in the figure on the…

A: Given,C1 : r = 4+322cosθC2 : r =2-22cosθand  r > 0 , θ∈ [ 0, 2π ]

Q: a) 2 B3] b) 001 010 101

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Q: 1. Determine the absolute extrema of f(x) = (cos x − 1) sinx on [0, π], if they exist, and identify…

A: As per our policy, we are allowed to attempt only first question. Kindly post remaining question…

Q: A. SOLUTION OF NON-HOMOGENEOUS SYSTEM GIVEN: 7 -3 4 0 -7] A = 2 1 -1 4 6 010-3 -3 -5 1.3 USE…

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Q: het Ley) = y(4) + y (3) _ 7 y (2) _y (¹) al solve: Lys = 36t-24et > b) solve: hy)= 36t-24et 2.2t c)…

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Q: 77 [(8-x1²- (2+x²) ² ]dx 1-2 663.5817

A: let I=π∫-228-x2-2+x22dx since the function is even , integral becomes I=2π∫028-x2-2+x22dx simplify…

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Q: nonhomogeneous system tY' = 2-2 Y + -2t (₁-²₁).

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Q: 3. Set-up the iterated double integral in polar coordinates that gives the volume of the solid…

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Q: Solve this problem. Show your complete answer with a graph in a given-required-solution format…

A: Here follow the graph of the region bounded.

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A: Given as, 4x2 - (y-3)2 + 4z2 = 4

Q: (h) Let u(x, t) be given by u(x, t) = a, cos(3nt) cos(2nx). [ an n=1 If u(x, 0) = cos(4x), 0≤x≤/2.…

A: This is a problem of Fourier analysis.

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A: Solution :-

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Q: b) The function y(x) satisfies the inhomogeneous second order linear differential equation d²y dy…

A: Variation parameter method

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Q: Find the area bounded by the curves -x + y² = 8, x = -2y and y = -2.

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Q: Inz) = Inr ei ) = Inr) + In ( e°0 )=ln r+iᎾ z = reie

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Q: 13. Let A be an invertible n x n matrix. Let E₁, . . . ‚Ek be elementary matrices such that E... E₁A…

A: Since, echlon form of invertible matrix is identity matrix.