c). Evaluate √√x² + y² ds along the curve r(t) = (4 cost)i + (4 sint)j +3tk, -2x≤t≤2π.

Q: 9. Determine y = Yc+yp using Non-homogenous equations: Method of Undetermined Coefficients Given: y"…

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Q: Q3/If f(x)=x²+1 and g(x)=√x, find the composite function and its domain: (a) fog (b) gof

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Q: (a) Given A = use the Cayley-Hamilton theorem to find (1) A¹-3A6+ A¹+3A³-2A²+31 (ii) A¹, where k> 0…

A: (a) Given A=2011 To use the Cayley-Hamilton theorem to find (i). A7-3A6+A4+3A3-2A2+3I (ii) Ak, where…

Q: 3 By direct partial integration, Solve the following PDES 8- Xx²z 5 4 4 JZ = 0, Z(X₂0) = x² + x, Z…

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Q: Solve the following systems of linear equations via matrix algebra: –3x + 2y – z = –1 6x – 6y + 7z…

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Q: Problem 1. Consider the differential equation dy 2x²+2 = dx X where y = 5 at x = 1. Use RK4 Method…

A: consider a differential equation dydx=2x2+2x with initial condition y1=5 use RK4 method to determine…

Q: Proving by Mathematical Induction A. 1. If P(2) = 1·3+2·4= 2(3)(11) 6 2. Prove that P(n) is true for…

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Q: Solve the given system by: a. LU factorization b. Cramer's Rule 2 -4 1 -4 0 3 -1 0 1 -1 3 Show…

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Q: Determine the total solution of the differential equation (D2+5D+6)y=6e(-3x)-100e2x O A. y =…

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Q: 3x 6 1 -In xy dx e-In √x dx +dy +=dx = e-mxx y X

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Q: 0 What is/are the correct explicit definition for {an} = 1, 2 3' 97 27... (choose all that applies)…

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Q: Find the general Solution of the following PDES • 3 их + 2 Иу U (x₂0) = 4x 2 e (3y-2x)/2 ans- u(x,y)…

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Q: 5 By separation of variables, Solve the following PDES :: ²4 ²4 dt² dx² 0 o , u(e,t) = u(5,t) =6…

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Q: Q.2 Check whether the following system given by its characteristic equation is stable or not and…

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Q: Determine the magnitude of the vector difference V' = V₂ - V₁ and the angle 0x which V' makes with…

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Q: 4 Find the general Solution of the following PDES • з Их + 2 Иу -Х ucx, c) - че 2 (зу-2х)12 ans3-…

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Q: 6 By Separation of variables, Solve the following 5 PDES :- d²4 d24 dx² 0 o u(e,t) = u(s, t) =6…

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Q: Set-up the iterated double integral in polar coordinates that gives the volume = 5. of the solid…

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Q: Find the Laplace transform L (cosht cos²t) @ & L (sinhst cashet) (2 3 L (sin't cos't)

A: Here we use the conversion of hyperbolic function to exponential function. And use some…

Q: in Column B. Column A 1. f(x-4)³dx 2. f(x + 1)³dx 3. f(x - 5)*dx 4. f(2x³-5) 6x²dx 5. f(x5 +1) 75x*…

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Q: Question 1 (Subspaces) For (a) and (b), show that these sets are subspaces of IR¹. (a) {(a,b,c):…

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Q: Q1\ A\ Define and give an examples with its solutions for the following terms: (1) Strongly…

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Q: EULER'S METHOD FOR SOLVING DIFFERENTIAL EQUATIONS NOMERICALLY y = f(x,y) y(x) = yo. Yn Yn-1 +…

A: The numerical solution of the differential equation is the value of the function that satisfies the…

Q: Find the general Solution of the following PDES ди -5X -3x 17 9 = 2 ди +u, ucx;o) = ду + 2 е ax…

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Q: Let xbe inner Product and ||x1|=|ly|| = 1 x+y Lix.y ? why?

A: Given that X is an real inner product space. x ,y be two unit vector from X then need to show that…

Q: fx) 0< x< n n < x < 2n < +2 Interval: 0<x<2*

A: Given function is fx=xπ,          0&lt;x&lt;π−xπ+2,  0&lt;x&lt;2π. We have to find the Fourier…

Q: [2 4 11 Q1/ Find the determinant of the matrix 3 8 5 16 2 41

A: Solution :

Q: We define a inner product in = U₁V₁ +2U₂V₂ + U3v3 in R³ for u = (U₁, U₂, U3) and v = (V₁, V2, V3)…

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Q: 2. Evaluate the double integral that will find the volume of a solid bounded by 21-2y²-322 and the…

A: Given that solid is bounded byz=1-2y2-3x2 and the xy plane,finding it's projection onto xy plane by…

Q: 5 By separation of variables, Solve the followin PDES :- du dt = 2 d2u dx2 @ o (4₂ t) = G U (0₂t) =…

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Q: 5S² + 25-4 (5+1) (S+₂) (S+ 3) Taking Laplace transform

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Q: (b) Let X=(2,3,5,8) with indiscrete topology and Y={a,b,c} with discrete, let f be a constant map…

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Q: (4) Let K be integer ring module 12 and let I=([4]) and J=([6]) be ideals of K. Then [2] belong to…

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Q: (1) Let I be a proper ideal of the commutative ring R with identity. Then I is a if and only if the…

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Q: dy Write down a differential equation of the form dt 13 solutions all approach y = as t → ∞o. 14 y =…

A: To answer the given question we will solve the differential equation dydt=ay+b and find the values…

Q: What is the negation of the proposition/statement: 9 14                                  b) 9 ≥ 14…

A: Solution :  Options (B) is correct

Q: • show that (x, y, z) = PDE : 2² + 8²4 дуг дуг + 2 x² + y² + z² = 0 824 dz² satisfies the

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Q: 7. Find the area of the region cut from the first quadrant by the curve r = 2(2 sin 20)¹/2

A: Solution :

Q: Set up the triple integral that will give the following: (a) the volume of R using cylindrical…

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Q: -7 y" - 4y² + 5y = f(t) Sy Y(s) = L {y (t)} -> (1) (2)

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Q: QUESTION 4 Calculate the area between y = 7 - x² and x-axis from x = -1 to x=2 as shown in Figure 1.…

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Q: 1 The Laplace transform of the solution of the following Cauchy problem ´y" (t) − y'(t) + 3y(t) =…

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Q: 3: A) Find the limits below x² + sin²y 1) lim lim (x,y) →(0,0) 2x² + y² y)→(1,1) x#y (x²-y² (x, y) =…

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Q: By direct partial integration, Solve the following 5 4 PDES 8- • Xd²z dz dy ₂ Z(X₁0) = x +X, Z (2,…

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Q: 2. Find the Wronskian of: a. -2x³ + 12 2x³ + 12 b. C. 0 d. Undefined f₁=x4 f₂ = -x4 f3 = x² f4 = -x²

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Q: The following problem involves an equation of the form = f(y). dy dt Sketch the graph of f(y) versus…

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Q: Find the general Solution of the following PDES ди -5X -3x 17 9 = 2 ди +u, ucx;o) = ду + 2 е ax…

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Q: Find the general Solution of the following PDES ди -5X -3x 9 = 2 ди +u, ucx;o) = ду + 2 е ax -5х-3у…

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Q: js(x) dx = (b-a) [ƒ(a) + f(b) -a) [¹ 2

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Q: 20 j ΣΣ (2k + 3) = j=5 k=0 = 2n+3 Σ (n + 5k)3 k=0 first step 2nd step final answer first step and

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