Solve the heat equation Ut = CUTI on the domaion 0< x≤ 2, t > 0, subject to u(x, 0) = -², ur (0, t) = 0, ur(2, t) = 0.

Q: 1. Evaluate the following Legendre symbols: (i) (ii) р 463 541 (iii) 8933 104729 (-).

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Q: Using the function f(x)=cos(x), on the interval: 0 (less than or equal to) x (less than or equal…

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Q: 1. Determine if the series converges. If it does, give the sum. 19 19 19 + 7 49 343 19

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Q: Since the first question has been solved, please solve the second question. Thank you!

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Q: Consider the predator/prey model x' y' 0): = = 3x - x² - xy -2y + xy. Find all critical points and…

A: Given predator/pray model is the following :So we get critical points for given system from which…

Q: Calculate truncation error for e^2 with two and three terms in taylor expansion

A: Truncation error formula The truncation error of the Taylor series approximation for  depends on the…

Q: (a) Use sensitivity analysis to determine the allowable range for C1 (b) Use sensitivity analysis to…

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Q: 2. Solve the following first-order differential equation. dy dx 4 (5 + x) y Initial condition y(0) =…

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Q: 2. Evaluate by listing the proper number of terms and adding them. k²-3 2 3. Evaluate by using the…

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Q: Write the following system of differential equations in matrix form. dx dt dy dt 15 = where Ū= = ||…

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Q: 3-6 Match the differential equation with its direction field (labeled I-IV). Give reasons for your…

A: To plot the direction field for a differential equation, we find the slope of tangents at different…

Q: 1. For the following equation show that x(x - 1)y" + 6xy' + 3y = 0 x=0 is a regular singular point;…

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Q: 2. Use Gauss' Lemma, to compute (²) = (-1)², μ = |aPn N, -6 (30). 31

A: We recall Gauss's Lemma and using Gauss Lemma we solve the problem.

Q: In a study of factors that influence brand switching by a certain demographic, the following factors…

A: Given the influence brand switching by a certain demographic, the following factors were identified…

Q: When a mass of 4 kilograms is attached to a spring whose constant is 64 N/m, it comes to rest in the…

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Q: 2. Consider the problem y = x - 10y (a) Verify that the analytical solution is y(x) = 0.1.x -0.001 +…

A: Solution:Given that, Now find the following:

Q: The coach of an age group swim team needs to assign swimmers to a 200-yard medley relay team to send…

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Q: A camera shop stocks eight different types of batteries, one of which is type A76. Assume there are…

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Q: 4. Solve the following ODE system using Euler's method, assuming that at x = 0, y₁ = 4 and 1/₂ = 6.…

A: Euler method is given by:yn+1=yn+hf(tn,yn)

Q: at equation aion 0≤x≤ 4, t-

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Q: T T T F 29. If x and y are real numbers and x² < y² then x < y. F 30. Let A, B, C and D be sets with…

A: We have to check whether the given statement is true or false.

Q: 41. Evaluate the line integral over the given curve C. (9x + 3y)ds; r(t) = (t - 9)i + tj, 0 ≤ t ≤ 4.…

A: We have to evaluate the line integral over the given curve C."Since you have posted multiple…

Q: 35. Find the area of the part of the plane 4x-2y-z4 that hesabuvo the root)c [-1, 4]X[3, 7]. a. 51…

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

Q: 47. Find the area of the surface. The part of the plane r(u, v) = (5u + 4v + 6)i + (3u + 3v + 8)j +…

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

Q: Write an equation for a rational function with the following properties: • Vertical asymptotes at x…

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Q: Find the coefficient on x^10 in each of the generating functions below. (h) (1-x^14)/(1-x)

A: Find coefficient of x^10

Q: Sketch the domain of the function f(x, y) = (x − 1)(y — 2) - √(y - x)(y- x³)

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Q: Consider the function ƒ (x₁, x₂ ) = 5 x² + 4 x² defined on (x₁, x2) = R². The function f (x1, x₂) is…

A: The objective of the question is to determine whether the function f(x1, x2) = 5x1^2 + 4x2^2 is…

Q: Suppose we are trying to show that lim f(x) = L where the graph of f(x) is given below. A distance…

A: For any  there exists  such that  i.e.

Q: Use diagonalization to find matrix A, assuming that A has the following eigenvalues and…

A: Given eigen value and corresponding eigen vector are

Q: 2. Find the fourth term of the expansion of (a + 2b)¹0 without writing out the entire expansion.

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Q: dz dt 0 1 10 z + 1 1

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Q: Find the shortest distance from the origin (0,0) to the hyperbola x² +8xy+7y² = 225. HINT. In the…

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Q: The graph of f(x) is given below. Select each true statement about the continuity of f (x) at x =…

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Q: Problem 4. (Flux) Given the surface M defined by the parametric formula r(u, v) = (u, v, u² + v²)…

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Q: and y(t) solutions. A B C Match the trajectory on the phase portrait to the correct x(t) D -2 y(t)…

A: To identify the solution curves, we need to check(i) The critical points (equilibrium points) in the…

Q: 5.1. THE LINEAR CONJUGATE GRADIENT METHOD 10 set of nonzero vectors {Po, P1, ..., Pi} is said to be…

A: Given that : Set of non-zero vectors    is  said to be conjugate with respect to symmetric positive…

Q: Using the First Derivative Test, what are the local maximum/minimum for the following function? f(x)…

A: Given function isWe know thatThe first derivative test is a method to determine whether a critical…

Q: Use MV = P(1 + RT) to find the maturity value (in $) of the loan. Principal $710,000 Rate (%) 13.35…

A: The given principal amount , rate of interest  and time  months.The aim is to find the maturity…

Q: T T T F 51. For any positive real number x, if x is irrational then √√x is irrational. F 52. There…

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Q: Solve the system of differential equations x₁= 2x1 + 0x2 x2 = −7x1 + 5x2 x₁(0) = 2, x₂(0) = 0 x₁(t)…

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Q: Use Stokes' Theorem (in reverse) to evaluate (curl F) ndS where F = 6yzi + 9xj +6yzeªk,S is the…

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Q: d) fln (x²)dx In e) fln (x²-1)dx In f) fx³ln (x²)dx

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Q: 2 2 2 Consider the matrix A = 0 2 0 0 1 3 (a) Find the eigenvalues and bases for the corresponding…

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Q: 5. Let A denote the set of all diagonal 2 × 2 matrices with real entries. That is, let A be the set…

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Q: #8: Use Divergence theorem to find the outward flux of F = (3x², e¹², cos³(x²+x)) of the cube in R³…

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Q: Find the value of integral 2+1 (y² +ix) dz

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Q: Given the following vectors u and v, find a vector w in R³ so that {u, v, w} spans R3 and a non-zero…

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Q: 5. Consider two general solutions of two different linear systems of equations X'(t) = AX(t): A.…

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Q: Use Stokes's Theorem to evaluate F. dr. In this case, C is oriented counterclockwise as viewed from…

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