Question: The polynomials p(x) = x(x − 1) and q(x) = ½ (x − 1)(x − 2) are orthogonal when the inner product is defined by (p(x), q(x)) = p(0)q(0) + p(1)q(1) +p(2)q(2). What is the distance between these vectors using the norm determined by the same inner product?

Q: prove that 11 ㅣㅣㅣㅣ 리 ZtZ3 < 1211 12월 18

A: For complex numbers z2,z3 with

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Q: Perform the operation if possible. -2 -1 -1 8 1 0 [339] 1 1 4 -1

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A: To calculate the proximity (distance) between two locations and the angles formed by these locations…

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A: We evaluate the integral by using different choices for b.

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Q: 7. Prove: For neN and F, the nth Fibonacci number, =Fn+1 (1) + (7¹) + ("z ²) + (~³²) +--+ (0) = ² 2…

A: “Since you have posted multiple questions, we will provide the solution only to the first question…

Q: Project: Modeling fish populations for Eco Fisheries, Inc. Eco Fisheries, Inc. operates a hugely…

A: Given  that :                      where are  constants and is  a  parameter very much less than…

Q: Using residues, evaluate the integral -8 x² (x² + 1)(x² +9) dx

A: Using residues, we have to evaluate the integral

Q: it If p(x)=2x²-3x+5, what is the remainder of p(x)+(x-5)? A) -230 B) 0 40 240

A: We, use division algorithm to find remainder.

Q: 1 Express the following in integer or rational form 64² × 273 x

A: Express the following in integer or rational form.Note: '' Since you have posted multiple questions,…

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Q: B = = v= -6 3 6 109 1 -37 -20 -2 -2 -2 1 2 is an orthogonal basis of Rª. Find [v] Fo

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Q: Consider the following matrix and answer the following questions: A = [11] 6 without doing any…

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Q: Given the function f(x) = 3x² - 2x on the interval -2<* ≤2 (a) Find the Fourier series expansion (b)…

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Q: into meters and centimeters

A: Given data from the problem are :Convert 9 yards 2.79 feet wide into meters and centimeters.

Q: Orthonormalize using Gram-Schmidt. -8 15 {[][]} ([181181)

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Q: Question 1. Consider the following function: a) Graph the function 3 2 0 ) = { $ 1-2 f(x)= 0≤x≤2…

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Q: √√₁²1² (2 In(x)-3) dx using six subintervals of equal width and one of the following. (Round your…

A: We just use the basic definitions

Q: Approximate proju and projw. -8 -7 -6 -5 -4 -3 -2 -1 proj u 5.491 projw 4.801 = vector u vector w -5…

A: Given thatWe have to approximate Projwu and Projuw.We know that

Q: (a) Is the operator dx a Hermitian operator? d² (b) Is the operator a Hermitian operator? dx²

A: (a) We have to check whether  the operator d/dx  Hermitian operator or not. (b) We have to check…

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A: The statement you provided is not necessarily true.If n vertices and exact  edges does not guarantee…

Q: 8. In solving the DE 2x²y"−xy'+(x² +1)y=0 about the ordinary singular point x = 0, it is found that…

A: The differential equation can be written asy″−12xy′+x2+12x2y=0Here the functions P(x)=−1x and…

Q: Mathematical Model for Fish Population Dynamics: The initial model equation, denoted as Equation…

A: Given  that :                      where are  constants and is  a  parameter very much less than…

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Q: (a) Prove that 2 and 3. are both primitive roots modulo 5.

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Q: Q-2) Find x(t) for the following DE➜ +4x(t) + 3 x(t) = 6 if x(0+) = 0, (0+) =0, using the Laplace…

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Q: € Question 3. A block of ice is in a container as shown below. The surface of the ice follows the…

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Q: and Assume |A| = 16, |B|=18, |C| = 28. If , how much is given |AnB| = 7 |AnC| = 11 |BC| = 8 AUBUC…

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Q: For the function f(x) = 9 - 5x², find a formula for the lower sum obtained by dividing the interval…

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Q: Sliding movement with a motor. A heavy block of mass 1 kg is placed on a flat surface and attached…

A: (a)Given that at t=1 seconds a motor exerts a force of t−1 N on the block. At t=4 seconds the motors…

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Q: Let ƒ : R¹ → Rk be a continuous function. Which of the following claims are true? Justify your…

A: Given that  be a continuous function.We know that a function  is a continuous function if  is an…

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Q: Suppose F is a sequence of increasing non-negative right continuous functions on [0, 1] such that…

A: Monotone Convergence Theorem theorem states that if fn is a sequence of non-negative measurable…

Q: Question 3.2. dr. (1) Let a, b € R be non-zero. Use integration by parts to determine faze d (Note:…

A: integration by parts:  If u(x) and v(x) are two functions then…

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Q: 7. Evaluate the upper and lower sums for f(x) = 2 + sin x. 0<x<T, with n = 2, 4, and 8. Illustrate…

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