Find the point at which the function f(r,y) = 2 in z+2 In y attains a maximum subject to the con- straint z+y==1.

Q: Find y as a function of a if y(0) = 7, y/(0) = -12, y'(0) = 108. y(x) = y" + 36y' = 0,

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Q: b) Consider the second-order truncation error (0 (Ax)2) with the step size (-Ax) and then, obtain a…

A: The truncation error is O∆x2 and the step size is -∆x

Q: Is g = {(x, y) ∈ [−5, 5] × R : x^2 + y^2 = 25} a function from [−5, 5] to R.

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Q: The cubic function y = ax3 + bx² + cx + d pass through (0, -6), (1, -2) and tangent to the line 3x –…

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Q: Solve the given optimization problem by using substitution. Find the maximum value of f(x, y, z) -5-…

A: Given  fx,y,z=5-x2-y2-z2 subject to z=4y. The given function is a function in 3 variables.  The…

Q: Let f(x, y) = x² + 5y². (a) Find f (5, 1) and f,(5, 1). fx(5, 1) fy(5, 1) =

A: Find

Q: F(x, y, z) = yzeX²i + e×zj + xyexZk, C: r(t) = (t2 + 1)i + (t² – 1)j + (t² – 4t)k, %3D 0 <t< 4 (a)…

A: Given,

Q: Suppose that f(æ, y) = e-3x² – 4y? + y Then the maximum is

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Q: Find the maximum rate of change of the following function at the given point. f(x, y, z) = x² + 5xz…

A: To Determine: find the maximum rate of change of the following function at the given point . Given:…

Q: The temperature at a point (x, y) is T(x, y), measured in degrees Celsius. A bug crawls so that its…

A:

Q: Calculate Vf when f 3x z-y7+ 4x'y+ 2x - 3y-5 at the point (1, 1, 0).

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Q: Use the second-derivative test to show that the function f(x, y) = x²eY – y²e* has a saddle point at…

A: A point (a,b) of function f(x,y) is said to be the saddle point if it is a critical point…

Q: c) Consider the third-order truncation error (0 (Ax )³) with the step size Ax and also (-Ax ) then,…

A: Both approximation is second order O((∆x)^2)

Q: The weekly revenue realized by a company is approximated by the revenue function R(x, y) = 550x +…

A: The weekly revenue realized by a company is approximated by the revenue function R(x, y) = 550x +…

Q: Differentiate the function. = In({ (4t+ 1)³ (4t-1)5 F'(t) = F(t) = In

A: The derivative of the function in the division form is given by the quotient rule which is given by-…

Q: Q4/ Linearize the Function Z = XY2 About X, = 3, Y, = 6 using: a) Absolute Variables b) Perturbation…

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Q: ƒ(x, y) = x¹y — x²y³

A: Please see the below picture for detailed solution.

Q: Let f(x) be a differentiable function. Explain why it is possible that f'(c)=0 for a function but…

A: Let f(x) be a differentiable function.

Q: find the critics (local max, lo cal min) Of the function f(xcy)= -x5+ Dy3+27x-24y+3

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Q: Let f(x) = e»in(²)+z² _ i) Find the x-values of the stationary points to the curve y = f(x), where 0…

A: The given function is  fx=esinx2+x2

Q: 10 X=-3

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Q: Find the work done when a particle moves along the x-axis from x= 1 to x= 3 under the action of a…

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Q: 13 Find the linearizatian z=L(x.y) f the function 2=f(x.y) =4x²-y²42y at the point (x.y) = (3,2).…

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Q: -1 A = 0 2) 0. x)T. F(e,) = ( 2

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Q: Consider the function ƒ(11, 12) = (2+1 − 1)² + (x1 + x2 − 1)². (a) Find the global minimum of f, and…

A: Please find the attached image.

Q: Check that the equation x³ + y³ + 2³ = x + y + z implicitly defines at least one differentiable…

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Q: Find the function r that satifies the following condition. r'(t)=(3t2,4t3,2t); r(1)=(-2,-5,-9)…

A: Given,          r't= 3t2 , 4t3 , 2t  , r1=-2,-5,-9