Show that if {Po, P₁, Pn} is an orthogonal set of functions on [a, b] with respect to the weight function W, then {0, ₁,.., n} is a linearly independent set.

Q: Example (2.3): solve the initial system ordinary differential equations by Runge- Kutta method f₁=y'…

A: Given that y'=1-x+3z ,y0=1, x∈0,1z'=x-siny ,z0=2 , h=0.2 at x=0.6

Q: Identify the coordinates of any local and absolute extreme points and inflection points. Graph the…

A: Since you have asked a question with multiple subparts here we will solve the first three sub parts…

Q: 6. For how many values of n will a regular n-sided polygon have interior angles with integral degree…

A: For an n-sided regular polygon, the sum of interior angles is n-2×180 In a regular polygon, all the…

Q: 2. Use f(x) = 2x + 5 and g(x) = x^2 + x - 6 for following combinations. A. (f+g)(x) = B. (g-f)(x) =…

A: Note: Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the question…

Q: b) Find the absolute relative approximate error for the second order polynomial approximation.

A: Solution

Q: Find f(2), ƒ(3), and ƒ(4) if ƒ is defined recursively by ƒ(0) = −1, ƒ(1) = 2, and for n ≥ 2 by (a)…

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Q: Find the solution set of the following. 2(1 + cos x) sin x -. tan X 2 x = [0, π]

A: tan(x/2)=2(1+cosx)/sinx tan(x/2)=((2sin(x/2))^2)/2sin(x/2)cos(x/2)        where 1+cosx=2(sin(x/2))^2…

Q: 4.1- You are building five identical pens adjacent to each other with a total area of 1000 m², as…

A: Given, Five identical pens are given below.

Q: Determine whether the given matrix A is diagonalizable. If so, find the matrix P that diagonalizes A…

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Q: Find the general solution to the following system of linear differential equations. The independent…

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Q: Consider the following region R and the vector field F. a. Compute the two-dimensional divergence of…

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Q: Which one of the apportionment methods studied does not violate the quota rule? Group of answer…

A: Let us solve the problem in the next step.

Q: Problem 4. Consider the vectors Vi -5 D-0-0-0 , V3 2 and v4= V2 = (a) Find a basis for Col A, where…

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Q: Problem 5. (a) Find the characteristic polynomial and the eigenvalues of the matrix -1 7 -1 = -[ A…

A: we have matrix A=-17-1010015-2 we have to find the eigenvalues and eigenspaces and diagonalize A.

Q: employee at a garden center fills a water tank once a day around noon to a height of 20 inches. The…

A: given function  Mx=5x3  and Tx=5x-103

Q: (4) Show that Trab) = a b Tr-Trace (5) Show that T. I = Tr(T) where I is an arbitrary second Order…

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

Q: Find a function  f(n)  that identifies the nth term  an  of the recursively defined sequence, as  an…

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Q: Define S to be the following relation on R[x]: S = {(f, g) = R[x]²: (x-3) divides (g-f) in R[x]}.…

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Q: 35. f(x, y) = 1 + y + x cos y at Po(0, 0), R: x ≤ 0.2, y ≤ 0.2 (Use cos y ≤ 1 and sin y ≤ 1 in…

A: Linearization of the function

Q: Find the number of equilibrium solutions of the r x' = x(y-2) โม่ = x − y

A: x'=x(y-2)y'=(x-y) Equilibrium solution of a system of differential equation X'=AX are those solution…

Q: In an election with 4 candidates, the 25 voters express the following preferences Number of Votes:…

A: In Borda count the points are allotted  Here there are 4 candidates, therefore 1 choice will get 4…

Q: The binomial distribution states that Prob(v successes in n trials ) = Bn,p(v) = n! v!(n − v)! Pº (1…

A: Introduction: Binomial distribution is one of the basic discrete probability distribution. Apart…

Q: The _____ is the linear function which represents the seller's cost of a product. Cost Function…

A: We need to fill the blanks of given statement. The _____ is the linear function which represents the…

Q: Determine if the matrix does any of the following: • A rotation • A projection • A reflection •…

A: From the graphical structures, we determine the type of matrices.

Q: 4. Let f(x, y) = y²exy. (a) Find the normal vector to the graph of f(x, y) at (0, 1, 1). (b) Find…

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Q: For the following questions, work out the answer by sequence: a. Given in y = f(x) = ln (1 + x³)…

A: Introduction: Maclaurin series is a special case of Taylor series. When we expand a function using…

Q: Does there exist an oriented simple closed curvey in the plane of length 2π such that fx dy-y dx >…

A: Given: A simple closed curve γ in the plane of length 2π To check: The existence of an oriented…

Q: Consider the following function: 3x 8x −1 -8x 3 2 -X 0 0 0 f(x) = -15 15 1 8 11 1 When f(x) is…

A: Given function is f(x) = 3x8x-151-1-8x15832-x110001

Q: I. Find the solution set of the following. 1. 2e23e + 1 = 0

A: The given equation is  2e2x-3ex+1=0 rewrite the equation as 2ex2-3ex+1=0 let ex=u therefore ex2=u2…

Q: Q6) Find the standard matrices for A and A' where T1 : R2 → R3 ,T1 (x,y)=(x,y,y) and T2 : R3 → R2…

A: These question related to matrix and linear transformation

Q: y(4) + 8y″ + 16y = 0

A: Given, y4+8y''+16y=0

Q: Given a 2-dimensional function T(x,y)=2y2+sin(πx) Find the expression for the partial derivative…

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Q: D = 2 O -1 -2 [0.5 0.5] 0.5 0.5 -2 -1 0 De₂ De 1 2 3 2 - -1 11 -2 -2 22 [0.866 -0.500] 0.500 0.866…

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Q: A 2 × 2 real matrix A with repeated eigenvalues satisfies the relation [i] = [-2], and has a…

A: Given, The relation  satisfies by the real matrix 2×2 with repeated eigenvalues is given by A01=0-2

Q: 04: Determine the convergence of tan¹(x) x²+n²In(n+2) , on A = [0, +00).

A: We have to determine the convergence of the given series of functions ;   ∑n=1∞an = ∑n=1∞tan-1xx2+n2…

Q: Suppose a graph has 8 vertices and is connected.  Three of those vertices have degree 6, and the…

A: Given: A graph has 8 vertices and is connected. Three of those vertices have degree 6, and the rest…

Q: Calculate the Fourier series of function f(x)=x^2 -L<x<L using the Fourier series of function…

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Q: SITUATIONAL ANALYSIS: Gardening has always been touted as a relaxing recreational activity that can…

A: Here we have given that Liza take 2 hour to plant 50 eggplants. So, in 1 hour she will plant, 502=25…

Q: Please go though every step and do not use a texblook solution. Why is the gcd(n-1,n)=1? why is n-1…

A: Why is the gcd(n-1,n)=1? U(n) be the group of units in Zn gcd (n -1 , n ) = 1  Because there is no…

Q: let f(x) be a function f:[0,1]→[0,1], f(x)=−4x(x−1). Let g(x):(−∞,∞)→[0,1] be a function such that…

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Q: A graphing calculator is required for the following problem. Gasoline is pumped into a cylindrical…

A: As per company guidelines we are allowed to solve maximum three sub-parts at a time so i am solving…

Q: Suppose the control problem is Maximize [(y-²)dt 0 Subject to y'=u and y(0) 10, y(1) = a = The…

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Q: Please solve the initial value problem and show your work clearly. Thank you.

A: Introduction: Calculus is a branch of mathematics that focuses on rates of change, differential…

Q: Suppose U = {{a, b), a, c, d, {a, d), e) is a universal set with the following subsets: A = {(a, b),…

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Q: f(x) = = 2, 2x² + 2x " X log₂ (x - 1), x<-2 −2 < x < 2, x‡0 x ≥ 2. 1. Sketch the graph of the…

A: Given function f(x)=2x&lt;-22x2+2xx-2&lt;x&lt;2, x≠0log2(x-1)x≥2

Q: Erin has a total of 20 bills, all of which are $10 bills and $20 bills. If her $10 bills were $20…

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Q: Find the limit of the following sequence or determine that the sequence diverges. n reat + 14n…

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Q: Find the eigenvalues and eigenvectors for 1   0      1…

A: Introduction: Eigenvalues are a unique set of scalar values connected to a set of linear equations…

Q: Solve IVP using the Euler's substitution: 4 ÿ' = [_† !]ÿ, y' y(0) = [²]. Solve using the method of…

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Q: 1.) Let 024 A = 655 10-3 052 B = 534 -2 4 -2 52 C = -24 (10) -4 1 D = 50 2-1

A: