The plane x + y + 2z = 2 intersects the paraboloid z = x² + y² in an ellipse. Use Lagrange multipliers to find the points on this ellipse that are nearest to and farthest from the origin.

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Q: 1. Find the Laplace transform of the function: f(t)= t¹3¹0-13cos³ (t) + et sin(10t) cos (13t)

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Q: 4. Consider the set R of real numbers and let * be the operation on R defined by a*b=ab-2a. Find…

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Q: Verify that the given function is harmonic and find its conjugate harmonic function.

A: According to our guidelines we can answer only one question and rest can be reposted.

Q: Using the values given in Exercises 1 and 2, verify that b f*f* f(x, y) dy dx = f*f*f(x, y) dx dy. 1…

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Q: The degree of precision of the quadrature formula Q[f] given by f(x) dx = Q[f] =1²f (²) - ƒ) +²1 is:

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Q: 8. Explain why in any group of 1500 people there must be at least 3 people who share first and last…

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Q: Q: Use the Second Derivative Test to classify the local extremes of the function f(x, y) = 10xye-(x²…

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Q: se the Sales information above to answer this question. he value x = 42.538 should be used in the…

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Q: a) Find all the real numbers à such the vectors 1- x 1+x and x+1 1 are orthogonal.

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Q: Q1/ If f(x,y)=find a unit vector u for which Duf (2,3) = 0 x+y

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Q: leccione una: a. x(z)= - b. x(z)= - c. x(z)= ■ d. x(z)= e x(z) = Z Z-2 Z 1-Z 1 1-2z-1 1 Z-2 1…

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Q: A linear programming formulation is below. Maximize 120T + 80C Subject to: 3T + 2C ≤ 200 2T + 2C…

A: to maximize 120T+80C constraints: 3T + 2C ≤ 200 2T + 2C ≤ 180 , ⇒T+C≤90T + C ≤ 40 -2T + C ≥ 0 -6T +…

Q: π 1 1 + 2 sin² x dx

A: Consider: ∫0π11+2 sin2x dx Now,  tanx =sinxcosx⇒sinx =tanx cosx⇒sinx =tanxsec x So, ∫0π11+2 sin2x…

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Q: The matrix. ^-[3] 3. A = has an eigenvalue of multiplicity 2 with corresponding eigenvector 7. Find…

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Q: The volume of a sphere is given by V =³, where V is th

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Q: For each of the following systems, find all the equilibrium points x₁ = x₂ a) (x₂ =−x₁ - x₂ + ² -X1…

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Q: Let V be R³ and TB = {n₁, n2, n3} and SA = {m₁, m2, m3} be the ordered basis fo 3 2 2 n₁ = - A , n₂…

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