Q.3) Find the constants a, b, c, d, e if f(z) = (ax³ + bxy² + 3x² + cy² + x) + i(dx²y - 2y³ +exy + y) is analytic.

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Q: x' = 2 -5 1-2, X

A: We will find eigen values and eigen vectors of coefficients matrix from given system and then find…

Q: f₁(x) = x₁ f₂(x) = x², f3(x) = 4x - 2x² g(x) = C₁f₁(x) + C₂f₂(x) + c3f3(x) olve for C₁, C₂, and c3…

A: f1(x)=x, f2(x)=x2, f3(x)=4x-2x2g(x)=c1f1(x)+c2f2(x)+c3f3(x) we have to solve for g(x)=0

Q: 1=₁x-e³dx Obtain the numerical integral of the integral by dividing the integral into 5 equal parts…

A: Given: I=∫36x·e3xdxWe have to evaluate the integral using the Trapezoidal method and Simpson's…

Q: (c) (1) (2) (3) (4) The following sketch shows AABC, with vertices A(p;8), B(-2;-2) and C. T(1;9) is…

A: Disclaimer: Since you have posted a question with multiple sub-parts, we will solve first three…

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A: given graph we have to find vector valued representation.

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Q: 0 z=-3 y=-√9-2² √9-1²-₂² S x=0 xyz dxdydz =

A: Triple integration is calculated as ∫z∫y∫xf(x,y,z)dx dy dz

Q: Consider a system of linear equations Ar=b that A is nxn. in n unknowns with augmented matrix (4|6).…

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Q: rove by induction that Σr(2-3r)=(n+1)(1-2n) r=1 VnEN

A: ∑r=1nr(2-3r)=n2(n+1)(1-2n) ∀n∈ℕ We have to prove by mathematical induction

Q: Suppose Goran places $6000 in an account that pays 8% interest compounded each year. Assume that no…

A: We know the Compound interest formula , A = P1 + rnnt    Here , P = Principal balance A = Final…

Q: Pusing Newton's approoch combined with Horner method find an approximation for groot in interval 3.…

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Q: 2. Let's consider these three autonomous differential equations: 1. = y²-2y II. y' = y² + 2y + 1…

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Q: The first three nonzero terms of the Taylor series for f(x) = cos x centered at a = π are (x-1)³…

A: Sol:- Taylor series of function fx at a is defined as: fx=fa+f'a1!x-a+f''a2!x-a2+f'''a3!x-a3+…

Q: Let S = V₁ = {V₁, V2, V3, V4, V5} where, ) 22 = , V3 = ₂V4 = V5 = 22 2 Find a basis for the space…

A: We have to find a basis for the space span(S) which is a subset of S. Then, we can proceed further.

Q: The point P(12, -5) lies on the terminal side of a trigonometric angle....Determine the exact value…

A: Here given that P(12,-5) The terminal side of the trigonometric angle  It is clear from the…

Q: Given is the amount M = {x R³ | x² + 9x ≤25, x3 = 0}. Tick all that apply: M is complete/closed. yes…

A: Since M contains all the points inside as well as on the boundary. Thus M is complete.

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Q: 1. Find the lateral area of the square pyramid. 2,5cm

A: Note: We’ll answer the first question since the exact one wasn’t specified. Please submit a new…

Q: or each magazine subscription she sells. Obviously this means that Linda will make (12)($4.00) =…

A: Introduction: One of the four fundamental mathematical operations, along with addition, subtraction,…

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Q: √√9-1²-2² ILT xyz dxdydz = z=-3 y=-√9-2² x=0

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Q: Given the supply and demand functions of good p = x² + 2x + 12 p = -x² - 4x + 68 Calculate the…

A: The supply and demand functions of the product are respectively, p=xS2+2xS+12 and p=-xD2-4xD+68 To…

Q: The first three nonzero terms of the Taylor series for f(x) = cos x centered at a = π are (x-1)³…

A: Given f(x) = cos(x)

Q: Part II: Problem Solving. Solve the following: 1. Consider the linear system a. b. 7x + 7 x 2 = 1…

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A: Given that the base of the tank is a square and shape of the tank is rectangular. Also base side…

Q: =4 м.) хаучн y = 52х Z= зу, Z=o

A: To Evaluate: The volume of the region bounded by the curves x+y=4, y=2x, z=3y,z=0.

Q: Using Laplace transform, solve y" - 3y' + 2y = 6 y(0) = 2 " y'(0) = 6

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Q: Gamma function Count! T(1/2)(3/2)(5/2)

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Q: B/ Put the following program in matrix standard form Min (z) = 10x₁+11x2 S.T. X1+2x₂ ≤ 150 3x₁+4x₁ ≤…

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Q: Q3: Michal has a 100-acre farm and plans to plant at most three crops A, B and C costs $40, $20, and…

A: Let the crop A is planted on  x1 acres crop B is planted on x2 acres crop C is planted on x3 acres…

Q: 3) Convert the following triple integrals to cylindrical coordinates or spherical coordinates (do…

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Q: a) 27 " dᎾ 5 + 4 sin 0

A: To solve the given integral  ∫02πdθ5+4sinθ

Q: . Define with example Injective Function Surjective Function Bijective Function i) ii) iii)

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Q: a. Solve by back-substitution: 3x1 + 3x2 + x3 = 12, -4x₂-3x3 = -10, 2x3 = 4. b. Solve by…

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Q: contour

A: For first Contour we use Cauchy Residue Theorem and for second we use Cauchy Integral Formula.

Q: x Question: 41 N = set of natural numbers. Let x, y = N. If x-y then x and y have the same remainder…

A: It is given that N is the set of all natural numbers. The relation ~ is defined on N as x~y if both…

Q: General Solutions and Phase Portraits. In each of Problems 1 through 6, find the general solution of…

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Q: a) 2-3u(t-5) cost = -t Find the 33 Ordine Lap of

A: The given function is ht=-t cos5t-3ut-5cost To find: the Laplace transform of the given function.

Q: Question 2 If a function f is continuous at 0, show that g(x) = f(x) is differentiable at 0 and find…

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Q: The Richter scale is used to describe the magnitude of earthquakes. The following equation…

A: We need to use the equation: logx=M derive a relation between x1, x2. Here, x1, x2 are the…

Q: solve the following linear programming problem using graphical method Max (Z)=80x+72y S. T: 5x+3y ≥…

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Q: Translate into English: a. ∀x(E(x) ⇾ E(x + 2)). b. ∀x∃y(sin(x) =y). c. ∀y∃x(sin(x) = y). d. ∀x∀y(x3…

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Q: Consider a system of linear equations Ar=b that A is nxn. in n unknowns with augmented matrix (Ab).…

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Q: Sketch and identify the curve defined by the parametric equations x = sin²t, y = 2 cost

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Q: A quadrilateral has the following vertices given: P₁ (1, 4), P2 (3, 4), P3 (3, 6), P4 (1,6). Find…

A: Let's draw the diagram as per given information, To find the coordinates of point X first find the…

Q: Solve the differential equation by variation of pa 2y" - 4y + 4y = ex sec x y(x) =

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