4 ( Find the extremum of f(x, y) = x²-2y² + 2xy + 4x subject to 2x = y, and verify that it is a maximum value.

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Q: Q1. Consider the improper integral S cos(x) (x+3)² dx. What type of improper integral is it, and…

A: Solution is uploaded below

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Q: 2) 1. a) Given the matrix A = ponding eigenvectors of A. b) Determine the general solution of the…

A: As per our guidelines,  we can answer only first three sub-parts. Kindly repost rest questions…

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A: Solution is uploaded below

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A: Given: is the angle between  and .To find: .

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Q: Use Lagrange multipliers to find the maximum and minimum values of the function subject to the given…

A: Given:To Find:Minimum and maximum values using Lagranges multipliers method.

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Q: #14 A spanning set Null A is {[]} ? A = 7 -4 -1 -4 0 Use comma seperated answers. if needed.

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Q: (a) (b) Consider the function f(x, y) = (x² + 4y²)5/2 Compute the partial derivatives fr and fy.…

A: Bartleby Guideline:-“Since you have posted a question with multiple sub-parts, we willprovide the…

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Q: Use the inverse matrices to find (AB)-1, (AT)-1, and (2A)-¹. 1-2 ----C -1 A-¹ = B-1 -2 5 (a) (AB)-¹…

A: To find:  and .

Q: st pls solve this question correctly in 5 min pls I will give u like for sure Mnty For a point (1,6)…

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Q: 4) Solvex(1+y²)¹/² dx = y(1+x²) ¹/¹² dy.

A: we use variable separable method to solve this differential equation.

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Q: What is the algebraic and geometric multiplicities of the eigenvalues of А.

A: The matrix .To Find:Algebraic and Geometrical multiplicity.

Q: In how many ways can four distinct numbers be chosen from the set {1,2,...,14} so that no pair among…

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A: Differential equation

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A: Let Substituting the value of y,y', and y'' in the given differential equation we havei.e.,

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Q: 1a) Sketch the graph of f(x) = -2 (x+1)^3 (x-2)^2 using zeros, y-intercept, and end behaviour. Label…

A: Note: As per the guidelines we are supposed answer only 3 subparts of a question. Please repost for…

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Q: Use the Linear Approximation to estimate the value. Compare with the value given by a calculator.…

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Q: Problem 2. Prove that there are infinitely many positive integer triples (x, y, z) such that x² +…

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A: We have to apply the Green 's theorem to solve the given problem.

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Q: Let u || Answer: and let W the subspace of R¹ spanned by {u, v}. Find a basis for W¹.

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Q: 4. Let A be a matrix whose singular value decomposition is given by (a) Determine the rank if A. (b)…

A: Bartleby Guideline :-“Since you have posted a question with multiple sub parts, we willprovide the…

Q: Find the moments M₂, M, and the mass m, of the triangular lamina defined by the vertices (0,0),…

A: Moments and mass of a plate with a given density , are given by the formula

Q: Find the area bounded by the curves y = x², x = 1, x and y=0 (the x-axis) Y 0 1 3 X

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