1. Find a power series representation for the function and determine its interval of convergence. X (a) f(x) = (b) f(x) = x² x4 + 16 2x² +1

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A: Find the vectors u and v whose initial and terminal points are given.        Initial Point  Terminal…

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Q: Consider the piecewise function 2+x² x<0 x=0 g(x) = 1, 2-³, 0<x< 1 2-x x 21 (a) For each of the…

A: note : As per our company guidelines we are supposed to answer ?️only the first question. Kindly…

Q: Prove 10^47+67 is not a prime(use Fermat's). Thank you :)

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Q: constants. ple 9.2. From y₁ = A2" + B(− 3)", derive a difference equation by eliminating the

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Q: 1. Find the Taylor polynomial of degree 4, centered at a 4 for the function f(x) = √x + 1.

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Q: 5. (8 points) Let A € M₂ (R) be given. (a) If det (A) = 1, prove that adj (adj(A)) = A. (b) If A is…

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Q: Vectors u and v are given by: u=5i-4j+pk v=2i+tj-3k (a) Express p in terms of t when u and v are…

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Q: ..) If an arrow is shot straight upward on the moon with a velocity of 73 m/s, its height (in…

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Q: 1. Let 1, y € R" be given. (a) If ||z|| = ||y|| = 1 and z-y = 1, show that z = y. (b) If ||z|| ≤ 1…

A: \documentclass{article}\usepackage{amsmath,amssymb}\begin{document} (a) Norm x=Norm y=1\\ Let angle…

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Q: 2 cos x Let f(x) 1 and g(x)= = = - 1-sinsin x find the inverse function of f(x) * g(x) sinx+tanx…

A: Given that,fx=cos2x1-sinx-1gx=sinx+tanx1+secxThe inverse function of fx*g(x) is determined as shown…

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Q: 8. Given the parallelogram ABCD below, with E and F the midpoints of sides AB and CD, AF||EC, and BP…

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Q: Verify that the points are the vertices of a parallelogram, and find its area. A(1, 1, 3), B(5, −2,…

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Q: 3:Use Gamma & Beta properties to evaluate : 2x¹e¹-* dx

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Q: Show that the compactness in satability theorem is neccessary.

A: The Stability Theorem fails when X is not compact

Q: In Problems 17-20, expand f(z) = annular domain 0 <z - 2 <3 N (z + 1)(z-2) in a Laurent series valid…

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Q: Find the zero-divisors of Z6.

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Q: 4. Sam invested $5000 in a high interest savings account and earns 3.5% simple interest per year.…

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Q: 10 0 01 det D = 64 2 4 15 5 21 03 01 det E-46 60 7 5 21

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Q: B: 3:Use Gamma & Beta properties to evaluate : f (In x) 3 dx

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Q: Find the value of following the integral: ☎ COS²T -π1+a* S². dx,a>0

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Q: Suppose that h is differentiable and h(x + y) = h(x)h(y). Find a formula for h'(x)consisting of a…

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Q: 3- A discrete topological space (X,T) is: a-To-space, b-T₁-space, c- T₂-space, d- No one.

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Q: QUESTION 6 Solve the following boundary value problems a. y"+4y= 0, y(0)=-2, y (7) = 5 6 b. y"+3y=0,…

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Q: 2. A firm uses capital, K, and labor, L, to produce output P according to P = KaL, a, 3 are positive…

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Q: Let f and g be functions which are differentiable on R. For each of the following statements,…

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Q: ar gaph? and what the chroma

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Q: 1. Prove that the following functions are quasi-concave: (i) f(x, y) = xy¹, x > 0, y> 0; (ii)…

A: Given: fx,y To find: Quasi-concave function

Q: 2. Let A € M, (R) be given. (a) If AA = 0, prove that A = 0₁. Does this hold if A € M₂, (C)? (b)…

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Q: Problem no10 Find gen. sol. I you +12y" +HOy² = 0 (0)²² (0)8 PPSH+vH¬"v

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Q: Let b be an inner product on the vector space E. 1) If b(u, v) = 2, |lu|| = 4 and ||v|| = 5 then…

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Q: 1. An indigenous farmer has a 400 feet of fencing and wishes to fence three sides of a rectangular…

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