Use the Divergence Theorem to calculate the surface integral F. dS; that is, calculate the flux of F across S. F(x, y, z) = 3xy²i + xej + z°k, S is the surface of the solid bounded by the cylinder y + z2 = 1 and the planes x = -3 and x = 1.

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A: ∫-∞∞7x2+4x+8dx

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Q: II. Show your solution completely. 1. Given f = x – 2x+3 and A =[-2,1], find |, f. J[-2.1]

A: To find the given integral

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A: (b) Given data given a differential equation y''+(cosx)y=0

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A: To sketch the position vector for the below vector. m=−4i+3j−5k

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A: Since you have asked multiple question, we will solve the first question for you. If you want any…

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A: We will convert the given system to a system of first order differential equations in matrix form.

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Q: Reduce to the form x + yi : 2 logsinh (-i+2) 40ežmi

A: We have to reduce following expression to the form x+yi :          logsinh-i+240e23πi Pre-requisite…

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Q: 2. (G VH) →(G AH) - (GAH) :- (GvH)

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Q: п — h n

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Q: Obtain the Fourier series of : f%) = cos 2x, weth mter val -IL<x 21e, ~ Graph the %3D diagream…

A: This is a problem of Fourier series.

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A: f(x) = x(8x49 - x) (x30 - 3)

Q: 6. f(x, y) = x³y + 12x² – 8y

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Q: (a) Let G be any group. Let H <G and K < G be subgroups with |H|= |K| = p, where %3D is prime. Show…

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Q: Question 1 1 -2 1 -1 1 2 -1 Let A = and assume that 1 2 -1 0 -1 -2 1 100 0 1 1-1 0 0 0 0 0 0 1 1 -1…

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Q: What is the iterative method in system of linear equations? 2. Give atleast two examples of each…

A: We can have this using given formula

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Q: 土

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Q: Q6. Use Taylor's Theorem to prove that if x > 0 then, 5 1+

A: Given,x&gt;0 To prove: 1+x12-1+x3+x29≤58!x3

Q: Using Euler's Method, approximate the initial value problem for various values of x given in the…

A: The formula for percent error is: PE = (|Estimated value-Actual value|/ Actual value) × 100 Or…

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Q: Question 5. Given the following recurrence relations, find their closed form. a. an = 4аn-1 — 4, ао…

A: Find the closed form of the given recurrence relations :-

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Q: Use Green's Theorem to evaluate the line integral. | (x - 4y) dx + (x + y) dy C: boundary of the…

A: The given integral is ∫Cx-4y dx+ x+y dy,  where C is the region bounded by x2+y2=1 and  x2+y2=16 To…

Q: 4. The diagram shows the point A(-5, -6, - 1) a) Name the coordinates of the points B. G D. G b)…

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A: Since you have asked multiple questions, we will solve the first one for you. If you want any…

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Q: dx dy 1. +у%3х, Зу dt dt

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Q: What is the iterative method in system of linear equations? 2. Give atleast two examples of each…

A: We can solve the 2 examples using jacobi formula

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A: Solution

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A: The defining characteristic of a linear transformation T: V \to WT:V→W is that, for any vectors…