Let V = P(¹) be the vector space consisting of linear polynomials, p(x) = ax + b, and (p, q) = ²^xp(x)q(x)dx be an inner product on V. (a) (b) Find all polynomials p € V that are orthogonal to p* (x) = x. Use part (a) to construct an orthonormal basis of V.

Q: 7. Show that if n is odd, then p(4n) - 2 q(n). =

A: 7. Show that if n  is odd,then phi(4n)=2phi(n)

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Q: A: Given the function f(z) = ez². Is the function Analytic? B: Evaluate cot-¹(+12)

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Q: sin(x) = x mx 110 (lerror] < 0.01)

A: We know thatsince this is an alternating series,then, by alternative series estimation theorem,we…

Q: Problem #4: Let Problem #4: A = 10 2 -2 -2 7 -5 8 -9 -2 3 -3 -9 -2 2 7 15 7 -4 Enter the singular…

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A: Let .Consider the linear optimization model (Pα,β)..Subject to:We need to write the linear…

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Q: Evaluate the indefinite integral. / COS X 5 sin x + 15 dx

A: This question is about integral calculus.

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Q: Determine whether the following sets are open, closed, both, or neither. 【a) (2, 3) U {4} (b) [2,3]…

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Q: (3) Suppose that G is a bipartite graph such that G = G(A, B). Show that G contains an even cycle.…

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Q: (c) Given that (2x², -π<x<0 g(x) = 0, 0<x<T is periodic function of period 27, by using integration…

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A: We know thatsince this is an alternating series,then, by alternative series estimation theorem,we…

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A: Given that  and  is harmonic.The aim is to find the function  such that is analytic on .

Q: Problem 6. I Let D2n = {e,r,r², ... n-1 -¹, s, sr, sr²,...,srn-1} be the dihedral group. Prove that…

A: Note we use the definition of normal subgroup to solve this problem.

Q: 2. 201 3. Σ. 1 n(x-5)" 4" 2n n=1 nn

A: Note: As per our guidelines, we can solve first question. Please repost the remaining questions.

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Q: Consider the following function. F(x)=²²a=0₁ n=3, 05x50.1 (a) Approximate f by a Taylor polynomial…

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Q: 7. 8. Another way of writing 5 = log41024 is a) 54 = 1024 Evaluate log525². a) 25 b) 1024 = 45 b) 4…

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