Minimize the function ƒ : R² → R given by f(x1,x2) = x² + 2×₁×2 + x² on the set X = {(x1, x2) Є R² : x1 + x2 − 1 = 0}.

Q: Suppose f(x, y) = x²-y-2 (a) On your solution sheet, draw contours of the function z=f(x,y)…

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A: a) f(x,y)=x+3xy+6x2+y2 is strictly convex.b) f(x,y)=−x2−2xy−y2 is neither strictly convex nor…

Q: FNSACC321/FNSACC322/FNSACC421 Assessment Monarch Institutes

A: Here's a summary of the key points:1. Competency-Based Evaluation: Students are evaluated based on…

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A: We have to derive the value of  from the first order condition of Lagrange multiplier method.

Q: What is the coefficient of 10 in the expansion of (x + 2) 15 + x4(x+3)16? Submit Randomize Reset

A: The required value of coefficient of x10 for the given expression is 472960488Explanation:

Q: (9) Find the general solution of 1 y" + =y' = 12 In(x) x2

A: The detailed solution with step by step explanation is written belowExplanation:Step 1: Step 2: Step…

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Q: Use Laplace transforms to solve the integral equation h(t) 4e 2 cost- - - I sin(t sin(t - x)h(x) dx

A:

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A: The parametrization is given asTo prove the parts (a) and (b) and further evaluate the value of t in…

Q: need help

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A:

Q: dy dx + 2xy + xy' =

A: The given differential equation

Q: Please do not rely too much on chatgpt, because its answer may be wrong. Please consider it…

A: Answer:  α=( 1 4 6 5 3 2 )Explanation:Step 1:

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Q: 3. Let TЄ L(C2) be a linear operator with only a single eigenvalue, λ = C. Show that p(T) = 0 €…

A: The proof is given using the properties of eigenvalue and eigenvectors.Explanation:Given:• T…

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A: For The statement is true for For :and The statement is true for

Q: 2z²+2 Q2: Find the Taylor and Laurent series of f(z) = = with center 0 z2-7z+12

A:

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Q: 3.- Find the general solution of the ODE "+3y"+3y+y=0

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A: It is a parabola opening upwardIs correct option.Explanation:If you have any questions let me know…

Q: Solve the given differential equation by undetermined coefficients. y" − y′ + ¼y = 8 + ex²

A:

Q: ) Calculate (8(x² - y)i + 8(y² + x)j³) · dř if: (a) C is the circle (x − 4)² + (y − 8)² = 25…

A: (a) We have to calculate  where .in parametric form Now  and Now

Q: 4. Prove that a subset of R is convex if and only if it is an interval. 5. Show that the union of…

A: Please see the explanation.Explanation:4. To prove that a subset of R is convex if and only if it is…

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Q: Plz Asap  Solve correctly

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Q: Find the Laplace transforms of the following functions: (a) (b) f(t)=esin 2t Y eisl => (x+) = S-x…

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Q: Find the general solution to 3x y" + 9y= e³x + secx.

A:

Q: 6. (Basis and Dimension.) Say P3(R) = {f: R → R | f(x) = ax³ + bx²+cx+d for some a, b, c, d = R}…

A: The objective of the question is to determine which of the two collections of functions, W₁ and W₂,…

Q: 4. (a) Show that {(2, 0, 1, 1), (-1,2,3, 1), (1,0,2, -1)} is a linearly independent subset of R¹.…

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Q: Q1: For v=2x²y + x2y-y³, check the function for Harmonic and then find f(z).

A:

Q: need help

A: Option (a),(b),(c) is correct See solution in image Explanation:

Q: Needs Correct and complete explanation.     Don't use chat gpt or  ai i definitely upvote you

A: The objective of the question is to find a unique solution to the 1-D heat diffusion equation for a…

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Q: 8. Sketch the graph of the following equations that are given in spherical coordinates (each of them…

A: The spherical coordinate system is given byAnd, We have the following relations:

Q: Use this digraph for the next 2 problems. Ti (3) T4 (12) T6(8) о T₂ (9) T7(10) о T5 (5) T3 (11) 3.…

A: 4) Time  : We identify ready task and assign to  and to Priority list :  Time  completes and no…

Q: Determine {f}, where f(t) is periodic with the given period. Also graph f(t). 2t, 0<t<3, f(t)= and…

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Q: Study the maximum and minimum points of the function f defined below

A: Given Differentiating partially,

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A: Given, that  is an integer such that  is cyclic.It is required to show that, for any  are both  and…

Q: Please do not rely too much on chatgpt, because its answer may be wrong. Please consider it…

A: Hence, we have proved both directions, and thus, the statement is true.Explanation:To prove the…

Q: Use the definition of the Laplace transform to find F(s) = L{f(t)}. f(t) = {2t+1 (2t+1 0 ≤t<2 3-t t≥…

A: See in detailsExplanation:

Q: d2 d 1 ed 1. [-/1 Points] DETAILS on tal system uthern Lube י BRECMBC9 14.1.007.MI. MY NOTES ASK…

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Q: A research report claims that mice with an average life span of 32 months will live to be about 40…

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