VI. Use Lagrange Multipliers to solve the following: Maximize f(x,y, z) = 4.x +2y + z subject to r +y +2² = 1.

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Q: 1. Verify Green's theorem in the plane for $ (3x2- 8y,dx + (4y - 6xy)dy, where C is the boundary of…

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Q: 3). For the following linear system of first order ODES dx 2x + 4y + 3z dt dy — 4х — 6у — 3г dt dz…

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Q: 10. Find the sum of the series 25 (a) 75 (b) 2 (c) (d) None of the above

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Q: 1. Determine whether f is Riemann integrable over (0, 1] and evaluate S f(z) dr whenever fE R(0, 1])…

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Q: Find the solution of the following Differential Equations 9) y"-y'-6y 0, y(0) = 6, y'(0) = 13.

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Q: 1.0 1,0 -8 for 0 <a <7, for 7 <x <8. Let f(x) Compute the Fourier cosine coefficients for f(x). Ao…

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Q: 1) Find the volume of the solid that lies between the paraboloid z = 2x2 + 2y and the plane z = 8.

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Q: Consider the problem of maximizing the algebraic expression q given by q = V6 – (x + 2)² – y²…

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Q: Other Math Question 2. Construct all the (isomorphism types of ) r-regular graphs, for total nodes n…

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Q: -Find the value of x for which Inx + (Inx)? + (Inx) + (Inx)* + = 9

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Q: (c) Let M be the surface with the equation r³ +y³ +z = 9 that is above the right triangular region…

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Q: 2) Consider a bicyclist whose position s(t), in feet, is given by the table where t is in seconds. t…

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Q: 4. Find the centroid of the region bounded by graphs of y = 4x – x², y = 2, and r = 0.

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Q: Q8: Given that -2 X = 1 8 -8 -9 -9,Z -7 7 -2. -8 5 what is the matrix 3X + Y – 3Z?

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Q: 10.Solve the given (matrix) linear system: 1 21 [1 X' 13 %3D

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Q: If f(x, y) = -x³ + y - 4xy - 7x2 - 6y, then in the process of obtaining its critical points we…

A: Critical points

Q: Q7: Solve for matrix X in the matrix equation 3X + B = C , where B and C are B -10

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Q: * For the following data (2,2,4,6,8,10,12) 7 12 4 6.29 10 6. Мean equal Median equal Mode equal…

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Q: Let f(x) = x²/4 be defined on [0,4]  . Use the a. RIGHT Riemann Sum b. LEFT Riemann Sum c.…

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Q: Prove that 17 is the only prime number of the form n²- 64.

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Q: modeling the motion of a spring-mass-dashpot system initially at rest and subjected to an applied…

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Q: Which of the following statement is false? (a) The characteristic of an integral domain is either…

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Q: 2 = In(x10y?) + Consider z as a function of the variables x, y which is denoted by ||u|| = V82. and…

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Q: Write the formal negation of the following statement: V r E D, x ¢ E.

A: Given: A statement, ∀x∈D, x∉E To write: Negative of given statement.

Q: What is the square root of -5?

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Q: -5 2 -3 In R° let z = 3 X = x= -1 and y = 2 6. 4 . Write z as a linear combination of x and y.…

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Q: 1 3 5. -2 ? Why? 5. -2 2 B = 3 -1

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Q: Exercise 6.1.8. Let G be a group and H <Ga cyclic subgroup of G. For any gE G, show gHg¯1 is cyclic.

A: Let G is a group and H≤G a cyclic subgroup of G.   To Show: For any g∈G, gHg-1 is cyclic

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Q: 7. Write the given system in matrix form: x' = (2t)x + 3y y' = e'x + (cos(t))y %3D

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Q: Solve the system using eit 1. - 2y + 2z = 3 2x – 3y – z = -7 -z + 3y – 3z = -4 %3D 2. a – 2y + z =-6…

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Q: Use a definite integral to find the area bounded by the curve x+3, the axes over the interval…

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Q: Determine whether the graph represents y as a function of x. Explain your answer. (a) y 4 2 -2 4 6.…

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