Compute the exterior derivative of the following differential forms on R": (a) x¹dx² ^ dx³. (b) e-fdf, where f = (x²)², (c) (-1)³x³dx¹ ^^ d^... ^ dxn

Q: The differential equation y"" + ay" +by" + cy' + dy = 0 has a solution y = -5test - 6e³t cos(2t) for…

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Q: Let x, y, z be (non-zero) vectors and suppose w = x - 3y + z. If z = x - 3y, then w = 00000 x+ Using…

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Q: A regional municipality is studying a water supply plan for its tri-city and surrounding area to the…

A: Present worth at year 2030Hence, present worth at year 2030 will be $158.147096 million

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Q: Consider the following. x = 6 sin(80), = 6 cos(80), 0 3 0 (a) Eliminate the parameter to find a…

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Q: At least one of the answers above A 9th order, linear, homogeneous, constant coefficient…

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Q: Tove that S L { cosh at} = 35 ₁² s>lal > 5-a² 2

A: In this question, we will find the Laplace transformation.

Q: 14. Derive the Newton's method for finding 1/N, where N > 0. Hence, find 1/17, using the initial…

A: We need to derive the Newton's method for finding , where .Using this, we need to find , using…

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Q: XA = In the figure shown below, the coordinates of A and B are known with values x₁ = 100.00m, YA =…

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Q: Problem #5: Consider the following five statements about similar matrices. (1) If A and B are…

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Q: of V = R¹X3. Find a matrix X E V such that Un W = span{X}. =[ X

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Q: 5: Find the Laplace transform of 3 + t5 + sin(πt).

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Q: Let f(x) := x² for x∊R, and let E := {x∊R : -1≤x≤0} and F := {x∊R : 0≤x≤1}. Find the sets E\F and…

A: Given, f(x) := x² for x∊ R,  E := {x∊ R : -1≤x≤0} and F := {x∊ R : 0≤x≤1}.

Q: What is the Laplace transform of sint cost? 1 OF +4 O O O 1 s+2 1 2t+2 1 2s+4

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Q: In a singular value decomposition of matrix A - V = 0.5 -0.71 0.41 -0.5 -0.5 0.5 U = 0.0 0.0 0.82…

A: The singular value decomposition of a matrix A of order m×n is defined as A=UΣVT , where U is a m×m…

Q: Prove that if A is an invertible n x n matrix, then adj A is an invertible matrix and -1 (adj A)-¹ 1…

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Q: Use the eighteen rules of inference to derive the conclusions of the symbolized argument below. Q S…

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Q: Use the elimination method to find a general solution for the given linear system, where…

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Q: Mark the following either true or false. Justification is required. For square matrix A, the (i,…

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Q: lims where S₁₁ = (¹+2√7 ₁ + 3 n+2. S, n n n+1

A: L'Hospital Rule : If limf(n)g(n)=00 or ∞∞ form , then Differentiate f and g with respect to x,  and…

Q: lim s n where s₁ = 1, and S n+1 = (1 – = -)Sn n+31 for n ≥ 1.

A: We first evaluate the first few values of the sequence

Q: Use the function pictured to estimate (a) The real values of x for which f(x) = 0. (b) The value of…

A: We will use the graph for find the answer.

Q: 1. Find the Taylor or Laurent expansion of the following functions at zo = 1 Z (1) z²-2z+5² (2) Z…

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Q: Write it again

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Q: Which of the following would best represent the statement "the plane is flying to the left of me,…

A: Which of the following would best represent the statement "the plane flying to the left of me, but…

Q: 5. Consider X with the discrete metric. (a) Show that every subset of X is open and closed. (b) Show…

A: Consider X with the discrete metric. (a) Show that every subset of X is open and closed. (b) Show…

Q: Find the roots of the following equation in [-, π], by using the Newton's method with accuracy 10-5.…

A: As asked we shall use MATLAB to find the roots.MATLAB code is as follows.1f = @(x) 2*x^2 -…

Q: 12. Let xo < x < < x, and let f be continuously differentiable. Show that a f[xo, x₁, x₂] = f[xo,…

A: A continuously differentiable function has a derivative at every point, and that derivative is…

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Q: Use the bar graph from the World View "Comparative Output (GDP)" to answer two questions. 20.6 0.01…

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Q: A couple received a $133,000 inheritance the year they turned 51 and invested it in a fund that…

A: Given thatA couple received a $133,000 inheritance the year they turned 51 and invested it in a fund…

Q: The function ƒ is defined by ƒ (x) = x³ – 5 sin (2x). Find all values of a that satisfy the…

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Q: 24.6 Let fn(x) = (x − 1)² for x = [0, 1]. (a) Does the sequence (fn) converge pointwise on the set…

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Q: This problem mainly tests your calculator skill. I would like you to do as much as you can on the…

A: A point of inflection on the curve at which the concavity change. i.e., the sign of the curvature…

Q: Let fn(x) = x^n for x ∈ [0,1]. check if it is pointwise convergence. Define where it becomes…

A: Given, fn(x) = xn , x ∈ [0,1].We will check poitwise convergence of fn on [0,1].

Q: It is not always possible to construct by ruler and compass, a square equal in area to the area

A: We have to show that It is not always possible to construct by ruler and compass, a square equal in…

Q: There is a circle whose radius r is changing with time t. We are interested in the area A of a…

A: (a) Area at We have given that now evaluated r and  at The initial area is

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Q: Use traces to sketch the surface: x² = 36y² + z²

A: Given surface :Use the traces to sketch the given surface

Q: Problem #1: Let Problem #1(a): Problem #1(b): 11 0 1 Problem #1(c): Select -4 0 (a) Find the…

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Q: Əre at' u(0, t)uo, u(x,0) = 0, 2² u k +r= Əx² (0 0), r is constant u(1, t) = uo, t> 0 0 < x < 1

A: Given pde:k∂2u∂x2+r=∂u∂tGiven conditions:u(0,t)=u0  ,  u(1,t)=u0   ,   t&gt;0u(x,0)=0   ,…

Q: Problem 1 Consider the set A of all strings of letters a- ● dcbac eba fe aba fa ● ● f of length 5.…

A: According to guidelines we can solve only first three subparts.

Q: c) 1. Most animals can walk 2. Everything that can walk is an animal 3. Something is an animal

A: Lewis Carroll's models for logic involve breaking down statements into universals and particulars,…

Q: Solve x(t) = = y(t) = = - → x' = y y = 18x + 3y help (formulas) help (formulas) x(0) = 0 y(0) = 8

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Q: Source Demand 1 2 3 4 1 108 M M M 10 2 1.09 1.11 M M 19 Destination 3 1.11 1.13 1.1 M 29 4 1.13 114…

A: Supply and demand are as follows:To Find:Using the transportation simplex method, determine the cost…

Q: Find the minimum norm solution of the underdetermined linear system 2x₁ + x₂ + x3 + 5x4 = 8, -x₁ -…

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