Eigenvalues: - Eigenfunctions: Yn || y" + xy = 0 with y(0) = 0, y(4) = 0. help (formulas) help (formulas)

Q: 1. Let B₁ = = {-1} {[]} i) Find Rep ii) Find Rep B1 and -{[]} B2 = be two ordered bases for R² C…

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Q: 4. For the following two functions f and g, determine go f and fog. f: R → R X →sin (3x) 9: R → R X…

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Q: erity following expressed polar co unctions, nd their domain of definition (the region that the…

A: Harmonic function using polar form

Q: Compute the line integral of f (x, y, z) = x^2 + y^2 − cos(z) over the following paths (a) the line…

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Q: 1. In each part of this question, you have been given a system of equations and the corresponding…

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Q: The payoff matrix and strategies P and Q (for the row and column players, respectively) are given.…

A: The payoff matrix and strategies P  and Q ( for the row and column players respectively) areWe have…

Q: A Cartesian and a polar graph of 6- r=1-4 cos (40) are given. Identify the points on the polar graph…

A: Given polar equation…

Q: Sketch the region of integration for O A. -9 Choose the correct sketch of the region below. 81- O B.…

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Q: Find producer's surplus at the market equilibrium point if supply function is p=0.7z+16 and the…

A: We have to find the producer's surplus at market equilibrium for a given supply and demand function.…

Q: Consider the shaded region in the graph below. Write SR f dA on this region as an iterated integral:…

A: (.)  Given iterated integral is,       where we will find the value of

Q: 6. If the complex number -2+3i is an eigenvalue of a matrix A = a, b, c, d are real numbers, then…

A: Given system of differential equation  and the eigen value is Claim:  is true

Q: Consider the complex function f(z)= 1/(z^2 +1)  Find the residue of f(z) at the pole z=i.

A: The residue of a function at a certain point in the complex plane is a complex number that describes…

Q: Wayne’s snowboard is 90 cm long. Luke’s snowboard is 120 cm long. i. Luke’s board is what percent…

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Q: 35 40 i The small ants first destroy the large ant colony in year The large ants harvest the fruit…

A: (a) We have to Construct a table showing each colony's population in years t = 5, 10, 15, 20, 25,…

Q: A mass weighing 20 pounds stretches a spring 6 inches. The mass is initially released from rest from…

A: The objective of the question is to find the position of the mass at different times, the velocity…

Q: Write the following set by listing its elements explicitly between curly braces: {x|x€z and…

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Q: 4. The behavior of the system is a sink, or a stable node. x' = x + y, y' = x + 2y

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Q: Let v = (x²z, 2 –— 2xyz − 3y + x²y, 3z − x²z) be the velocity field of a fluid. Compute the flux of…

A: The Divergence Theorem converts a surface integral of a vector field over a closed surface into a…

Q: Prove that if R is an integral domain of character- istic p where p is a prime number. Then for any…

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Q: 2 f(x) 2 (6,2) R 20 6 g(x) 8 X 2 and y The functions f and g are given by y = √x = 8 - x. Let R be…

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Q: Prove that the d₁ ("Manhattan") metric on R2 is really a metric.

A: The objective of this question is to prove that the d1 (Manhattan) metric on R^2 is indeed a metric.…

Q: T T T T F 18. Let A and B be sets then A + B if, and only if A ¢ B and B ¢ A. For sets A, B, and C,…

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Q: Solve the following problem and show your complete solutions. Explain your work for better…

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Q: 2. Let T: P₂ (R) → P₂(R) be defined by T(p)(x) = p(0) + p(1)(x+x²). (a) Prove that T is…

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Q: 13. Two airplanes depart from the same place at 2:00 p.m. One plane flies south at speed of 376…

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Q: vector field in the plane,

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Q: Prove the conjecture bn= 2(bn-1)+1, n>=3 using strong induction. Recurrence is given bn=3bn-1-2bn-2…

A: We shall solve these question by use of induction

Q: (12) Let f(x) = 17x5 + 3x + 2x +9 and g(x) = x³ + 2x - 1. (b) Compute the quotient and remainder…

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Q: At a local college, four sections of economics are taught during the day and two sections are taught…

A: At a local college, four sections of economics are taught during the day and two sections are taught…

Q: Construct an 80% confidence interval estimate for the population mean given the values below. a=47 n…

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Q: 6. Given tan (0 - 450) = 4, find tan 0. D

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Q: Use the divergence theorem F = tan−¹(5y + 8z)i + graphs of z = √√x² + y² to find the outward flux…

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Q: Vector field F is given by F(r) = (x, y, z + 1) and surface A is the locus of points satisfying z +…

A: The given vector field is .The given surface  is the locus of points satisfying  for .We need to…

Q: Jane invest R8000 at an annual interest rate of 6% continuously compounded annually. how much will…

A: Here in this question we have to find how much will her investment be worth after 5 years. where the…

Q: Use the Direct Comparison Test to determine the convergence or divergence of the series co 872 Σ x=0…

A: The given series is .To use the direct comparison test to determine the convergence of the…

Q: Suppose R is the shaded region in the figure, and f(x, y) is a continuous function on R. Find the…

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Q: Use series to approximate the definite integral to within the indicated accuracy. ²*x lerror <0.001…

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Q: 3 Integrate f(x,y,z) = x + √√y - z³ over the path from (0,0,0) to (3,9,3) given by C₁: r(t) = ti +…

A: The given function is,Let,Also the given paths are,So,

Q: 2 B= [11] 3 -1 Write B and B-¹ as products of elementary matrices.

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Q: Find all eigenvalues and eigenvectors (up to scaling) of the matrix (a) over R (b) over F3 2 viewed:…

A: Using characteristic equation we find eigenvalue

Q: Let A be a diagonalisable 3 x 3 matrix with rational entries. Working over R on V = R³: (a) Is it…

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Q: Find the equation of the tangent line for the following function. Then plot the original equation…

A: The given parametric equations  and .The aim is to find teh equation of the tangent line to the…

Q: Two independent random variables are defined with the following distributions: X p 1 2 3 (a) 0.5 0.2…

A: It is given that  and  are two independent random variables with probability distribution…

Q: Find the eigenvalues 2 and eigenfunctions yn(x) for the given boundary-value problem. (Give your…

A: Given differential equation

Q: Find the optimum strategies for player A and player B in the game represented by the following…

A: The given payoff matrix is .

Q: Suppose R is the shaded region in the figure. As an iterated integral in polar coordinates, B D f…

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Q: Solution is incorrect

A: We have to calculate the double integral of  over the triangle indicated in the following figure

Q: W#9-2.4 Sinusoidal Functions UPAN 1 attempt remaring. Find a formula for the graph of the function y…

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Q: a) Let p=13. Compute L2(3) b) Show that L2(11) = 7.

A: Here concept of field is used.

Q: 1. Solve ut = 9ue sin 3x for 0<x<, with u(0, t) = u(x, t) = 0 and the initial conditions u(x, 0) =…

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