Solve the IVP dx -12 6 dt = =[ 3]x, x(t) = x, x(0) = 181. A

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Q: (a) the quarter-circle C₁ from P(1,0) to Q(0, 1): r(t) = (cost, sin t), 0 ≤ t ≤ (b) the…

A: These are the questions from the subject, Vector Calculus.

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Q: 4. Prove by induction that 3" ≥ 2" +n for all n ≥ 1.

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Q: Prove that : (1-2xz+z²) 2 Σ (2n +1) P₁, (x) z"

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Q: Expand x" in a series of Hermite polynomials.

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Q: Orthogonal Properties of Legendre's Polynomials : L, Pm (x) P₁ (x) dx 2 2n + 1

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A: Given, A=2-7-54   We have to find basis B.

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Q: Problem 5. the Ratio Test. (a) 8 n=1 πn n! State whether each of the following series converges or…

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Q: 5.6.35. Prove that the set of all finite subsets of N is a countable set. Hint: For each k = NU {0},…

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A: The function fx, y, z=xyz over the region bounded by x=0, x=4, y=0, z=0, and y=4-z2. We have to…

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

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Q: Let f (x) be a polynomial function with a zero of multiplicity of 1 at 3 and a zero of multiplicity…

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Q: Use the method of undetermined coefficients to solve the nonhomogeneous linear system *-[1]+[+] X -t…

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Q: Find the power series of f(x)g(x), given f and g as defined. f(x) = g(x) =  ∞     n = 1   x 3   n…

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Q: The unit step function IR→ R is defined as if x 0. I(x) = 0 1 (i) Let s € (a, b), and suppose f :…

A: Note: We will be solving part (i) as mentioned. Given that s∈a,b, and suppose f:a,b→ℝ is bounded on…

Q: ) Write a proof of the following statement: If λ is an eigenvalue of a real square matrix A, it lso…

A: We can prove the given statement.

Q: aplace's Second Finite Integral for P, (x): P₁ (x) = -√5₁ de 72+1 [x ± √(x² - 1) cos 6] ¹+¹' nEN

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Q: Solution (incorrect!) (i) Group G: Modular multiplication is commutative, so G is abelian. Hence, by…

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Q: rove that: 1-z² (1-2xz+z²)2 3 32 2 11 Σ (2n +1) P, (x) z" n=0

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Q: Find the laplace transform of the following. 1-) f(t) 3 3U(+) + = 2.) fl+] 3.) h(t) = + 8(+-2) +…

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Q: Suppose that y varies inversely as the square of x, and that y = 9 when x = 14. What is y when x =…

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Q: 1 -B 1 Consider the following subsets of R³. Determine if they re subspaces or not. Support your…

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Q: (a) Find dy dx (b) Find || dy dx d²y dx² expressed as a function of t for the given the parametric…

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Q: Problem 2. (i.e. 1+¹=1). Let p be a real number such that 1 0, and the function Tf is continuous on…

A: Since you have asked multiple questions, we will solve the first question for you. You may post the…

Q: Find functions g and h such that f(x) = g(h(x)). f(x) = e4x + 2 A. g(x) = 4x+2, h(x) = ex OB. g(x)=…

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Q: Answer without referring back to the text. Fill in the blank. For the method of undetermined…

A: Sol:- Apply particular solution sum rule:   If yp1t is a particular solution for…

Q: Find the B-matrix for the transformation x-Ax when B=(b₁,b₂, b3}. A= -7 -72 1 17 -4 -72-21 The…

A: Solution :-