Let B = {1+x,1 – 3x?, x + 6x?} and p(x) = 12 + 8x + 9x?. You are given that B is a basis for IP2. If [p(x)]B= |B|, then the value of 3 is

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A: This is a problem of series.

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Q: Q5) Find volume of body bounded by z =x-y from below and z = x +y from Above inside y = x²,y = 2.

A: Volume bounded by the region

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A: Solution

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A: In polar coordinates  x=r cos θy=r sin θdxdy=r dr dθ

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Q: Let A = ⟨1, 0, 2⟩ and B = ⟨6, −2, 3⟩. Solve for projAB. Then, find the angle between projAB and B

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Q: 2. Solve the following differential equations: (a) y' e2y = (b) y' = 1+ Y (c) xy' = y(3 – x)

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Q: Petermine whether the following series is convergent or divergent (-1)"3n² 4n²–1 (b) n=1

A: Given series is ∑n=1∞(-1)n3n24n2-1

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Q: L{t cos²5t }

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Q: Show that if x is an integer, then gcd(x + 1, x2 – x + 1) divides 3. -

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A: This is a problem of Taylor series.

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Q: (b) If the power series An(x + 1)" converges at x = 2, then >(-1)"an converges. n=1 n=1

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Q: Determine whether the following series is convergent or divergent (-1)"3n 4n²–1 (b) ) n=1

A: Using Leibniz alternating series test.

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Q: -2n2n 2n n 2) п En=1 1 —

A: Given series is ∑n=1∞1-2n2nn2n

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A: This is a problem of vector Algebra.

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Q: Question 10 Let u(x,t) be the solution of the partial differential equation u, =Ux 00 with the…

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Q: Determine whether the following series is convergent or divergent 3- Vn (a) Vn3 n=1

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Q: Define Euler's P-function. Showing your working, compute (5), D(23) and (115).

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