Calculate the following double integrals and draw the region of integration.

Q: Estimate the volume of the following solids by Riemann sums m n V=f(x, yj) AA ~ΣΣ i=1 i=1 Estimate…

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Q: 4) Prove that y = x-3/2 is a solution to 4x2y" + 12xy' + 3y = 0.

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Q: If d³p dq³ d²p dq² + p = 0, what would be the order of each differential term?

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Q: EX: Find all residues of f(z) = Sol: there are f(z)= 50 Z 11 11 (Z+4) (Z-1)² 50 Z 32²² +42-7JZ=-4…

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Q: f(x+0.0001)-f(x) Use 0.0001 f(x) = -3x² 6x at x = -5.9 6.1 -6 6 4 to determine the instantaneous…

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Q: 2. A firefighter who weighs \(192\) lb slides down an infinitely long fire pole that exerts a…

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Q: Excercise 5 (Evaluation of the integral from below). Let d be a positive integer. Consider the…

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Q: Investigate the relationship of Fibonacci numbers with the Golder ratio. 1,1, 2, 3, 5, 8, 13, 21,…

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Q: with 1 element x. How *x is ... and there is on obviously, it is commu- elements, ₁ and 22. Dinary…

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Q: x² (d) √ √ 1 - 4.² (HINT: sin² t = ½(1 – cos 2t).) dx. Evaluate

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Q: 2.11 Determine whether the following set of vectors is linearly independent: A = 2ê1 - ê2 + ê3, B =…

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Q: a) By using the substitution u = √√x +3, evaluate S. 2 √(√₁ + 3)2 d. dr.

A: Given, ∫142xx+32dx

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Q: if y(x) is the solution of the differential eqution xdy - (y² - 4y) dx = 0 for x > 0, y(1) = 2 and…

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Q: In each of Problems 11 through 14, find and plot both the steady periodic solution xsp(t) = C cos(@t…

A: Given : x''+6x'+13x=10 sin5t       ;  x0=x'0=0 To Find : Steady periodic sol and actual sol

Q: 3. f(18) 22, f(19) 35, f(20)=60, f(25)=80 Prepare an overdetermined system using quadratic…

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Q: Evaluate (8) [a² √² + 1dz (c) x3 (a) [ sin(sin a) cos rdr (b) tan-1 X dx 1 + x² [²

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Q: Prove (1.2), (1.3), and (1.4).  

A: (a) Let x∈A∪B So, ⇔x∈A or x∈B⇔x∈B or x∈A⇔x∈B∪A So, A∪B=B∪A

Q: Three sets have 5, 10, and 15 elements, respectively. How many elements can their union and their…

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Q: 2.13 Using the Gram-Schmidt orthonormalization associated with the following sets of vectors: (a) e₁…

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Q: Solve the Following initial value problem X-2x (५(५) 12 dy ग्र ५०) =1 S T

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Q: 5. Find the general solution of the differential equation. 21xy' + y = 462X

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Q: Q4. Solve the partial differential equations by the method of separ. un of variables: (i) py³ + q x²…

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Q: 24.If the functions y1 and y2 are a fundamental set of solutions of y″ + p(t) y′ + q(t) y = 0, show…

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Q: If F = (x + y, x² - y) a= y = √, calculate fr F.Tds by using computing the line integral directly.)

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Q: 1. Is (, (-2) ³) = (1, −8) ? 2. Let S = {2, 4, 6} and T = {1,3,5}. Use the set-roster notation to…

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Q: 11. Prove that if d divides a, then dk divides ak for every positive integer k.

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Q: Investigate the relationship of Fibonacci numbers with the Golder ratio. 1,1, 2, 3, 5, 8, 13, 21,…

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Q: The equation f(x)=x^2-10=0 has a root near x=3.   a) Apply four iterations of the Secant Method,…

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Q: 1 0 6- 1 1 1 2 2. Having computed A from #1 above: 1. Write down the equation of the best fit line…

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Q: 6. Consider the eigenvalue problem y" + ày = 0; y'(0) = 0, y(1) + y'(1) = 0. All the eigenvalues are…

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Q: Here ê, are orthonormal unit base vectors in R³. 2.12 Let the vectors (i, j, k) constitute an…

A: Given: Vectors are  e1=-i^-j^e2=i^+2j^-2k^e3=2i^+j^+k^ To find: (a) the dual or reciprocal…

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Q: (b) If f(r) = (+1), show that f(r)-f(r+1) = (+1)(+2). Hence, or otherwise, find Σr (r+1)(+2)

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Q: Write each of the following arguments in symbolic form, then state the validity of the argument with…

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