The conjugate harmonic function v(x, y) of u = In (x² + y²) is

Q: Show that X is Hausdorff if and only if the diagonal △ = {(x, x)|x ∈ X} is closed in X × X.

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Q: 2) Consider the following system: x + by = 9 a₁x +9y=-27 Determine the value(s) for a for which the…

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Q: Find the roots of the auxiliary equation: 2D4-4D³-23D² + 12D + 36 = 0

A: Given differential equation is 2D4−4D3−23D2+12D+36=0. We have to find the roots of the auxiliary…

Q: Q3) Find the root of the equation F(x)=x²-3(sinx)² by using Newton Raphson method with initial value…

A: Newton Raphson method Steps Step-1: Find points a and b such that a<b and f(a)⋅f(b)<0.…

Q: =-(-₁ 0 Given that A = 100 = a) eAt - Akt k! b) PDP-1 Method ; c) Laplace Transform. 0 , compute eAt…

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Q: 8) Evaluate dA, R: 1st quadrant bounded by y² = x & x² = y R 9) Evaluate ff sin (y) dA, R: the…

A: As per our guidelines we are supposed to answer only first question.kindly repost other parts. Thank…

Q: dy a) Show that the equation x² - 19y² 18xy = is homogeneous. dx The equation is homogeneous because…

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Q: For the function shown f(x)=x/L, where L=1. f(x) 1 L/2 L If the function is expanded in terms of a…

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Q: (a) Can we apply Rolle's Theorem to this function? If yes, explain what is the conclusion; if no,…

A: The solution follows from applying the defition directly. The detailed solution is presented below.

Q: Q4\ Solve by Gaussian elimination x - 4y-2z = 21 2x+y + 2z = 3 3x+2y-z = -2

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Q: Solve by picard method (up to four approximation) y' + y = e* and y(0)-0 Find y(0.1)?

A: We have to find the solution of the given problem.

Q: Find the solution of the differential equation using L.T: y'(0) = 1, y(0) = 0 y" +9y = 20e-t

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Q: Q2:/Sketch the region (R) of integration f (x² + y²) dydx and evaluate the integration. Then reverse…

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Q: Q2:/Sketch the region (R) of integration f (x² + y²) dydx and evaluate the integration. Then reverse…

A: We have to sketch the region R and reverse the order of integration and then we have to evaluate the…

Q: 1- Solve dx = cos x + y, where y = 2.0 at x 0 take step size h = 4x = 0.1 and solve for 0 ≤ x ≤ 0.2…

A: The solution is given by using the fourth order Runge kutta method as follows in details.

Q: 2 Let w = z². Find the image of the first quadrant in z-plane

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Q: Q1/ Find -1 = s² (s+1)(S-1)²

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Q: Let T be a compact operator on a Hilbert space H and (n) be a sequence o complex numbers. Suppose…

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Q: 1. Write the solution of the system of equations: P₁ = 5p₁ - 4p₂ + e²t; p₂ = P₁; P₁(0) = 2/1, P₂(0)…

A: Given system is p1'=5p1-4p2+e2t,     p2'=p1   Also given p1(0)=32,    p2(0)=-11   To Find: Solution…

Q: Find the values of x and y - SX+(s+6) Y=1 ....... (3-s) X-2sY = -8 ...... (1) (2)

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Q: Find a. b. [ f(z)dz. if C 1 f(z) = z sin z f(z) = 2² - z+1 z²(z - 1) and C:|2|= 1 to positive…

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Q: Consider the function f(x) = 2/x. Calculate the second derivitave at x = 2 numerically using central…

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Q: (²+1) ecosx cotx y² dy cosx dx

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Q: 2. Given is the distance between an important city in Malaysia. The table shows the cost of…

A: As an application of graph theory, It can be seen that A)Shortest route The shortest path from (1)…

Q: Prove Bernouilli's Inequality which states: If x ≥ −1 then (1 + x)” ≥ 1 + nx for all natural numbers…

A: To Prove: Bernoulli's Inequality which states: If x≥-1, then (1+x)n≥1+nx for all natural numbers n

Q: (f) What is the first-order condition implied by unconstrained maximization of I1 X 1333 X, where x…

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Q: Jatrix |AJ = 6 2 he rank of matrix is 3 4 10 7 1

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Q: 1) Using Laplace transform methods, solve for t20 the following simultaneous differential equations…

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Q: (m) dy dx y separable exact linear in x linear in y homogeneous Bernoulli in x Bernoulli in y none…

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Q: Q2. Use the Newton Backward interpolation formula to compute f (-0.92) from the following data. -2.0…

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Q: A tank contains 350 liters of fluid in which 20 grams of salt is dissolved. Pure water is then…

A: It is given that a tank contains 350 liters of fluid which contains 20 grams of dissolved salt. Then…

Q: 1. Gaussian integral The Gaussian integral, which has useful applications in probability…

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Q: Q4) find the soluation of differention equation using exact equation 2) 2xy' = 10 x³y5+y

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Q: Find all integer values of x for which 3x = 4 (mod 8).

A: given congruence equation 3x≡4(mod 8)

Q: Given that f(x)={kx2+2,≤22kx,x>2. If limx→2f(x) exist, then k equals.

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Q: B)Z = 1+ Ini, find |21.

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Q: Evaluate the following integral: fa-e²¹) dx a. Analytically b. Trapezoidal rule c. Composite…

A: Let us start solving the problem step by step

Q: The approximation of the integral f(x-1) cos(x-1) dx using two points Gaussian quadrature formula…

A: Given integral is ∫−11x−12cosx−1dx. We have to approximate the given integral by using two point…

Q: The surface of many airfoils can be described with an equation of the form xa₁x y ‚ = + 0 = ₂2 [²₁…

A: You can find matlab code and answer for this problem in next step

Q: Ⓒseparable exact linear in x linear in y homogeneous Bernoulli in x Bernoulli in y none of the above…

A: Here we have to check for all the condition which can be possible.

Q: * solve the system of equations by jacobi's iteration method 10a -2b-c-d=3 -2a+10b-c-d=15…

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Q: Consider the autonomous differential equation dy/dx = fy), where the graph of fis given. Use the…

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Q: Determine the following limits by using L'Hôpital's Rule, if exists. 1- x + ln x (a) lim 1³-3x+2 (b)…

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Q: Determine the following limits by using L'Hôpital's Rule, if exists. 1- x + ln x 4/3 X (a) lim x1 x³…

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Q: Find dy dx II - for the function y = 17x. dx

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Q: How much should Shane have in a savings account that is earning 2.50% compounded monthly, if she…

A: Given information Regular withdraw d=$1,900 Interest rate r=2.50% ⇒r=2.50100=0.025 Number of…

Q: 7. Find the eigenvalues and eigenvectors the system X' = [₁ 30. Use the eigenvalues and eigenvectors…

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Q: solve the system. Y₁ The initial value problem Y₂ Y₂ Y""(t) + 3Y"(t) + 3Y!(t) + Y(t) = -4 sin(t),…

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Q: In this problem, x = C₁ cos(t) + C₂ sin(t) is a two-parameter family of solutions of the…

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Q: Q2\ Solve by picard method (up to four approximation) y' + y = e* and y(0)-0 Find y(0.1)?

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