4x 28. If R = and errors in x, y, z be 0-001. Show that the maximum relative error at x = y = z = 1 is 0-009.

Q: Find the values of x, y, z at which f (x, y, z) = x2 + 4y2 + 5z2 - 6x + 8y + 3 assumes its minimum…

A: f(x, y, z)=x2+4y2+5z2-6x+8y+3   we have to find all points of x, y, z Taking, ∂f∂x=0, ∂f∂y=0 and…

Q: Let y = 3x + 2x + 4. If Ax = 0.4 at x = 1, use linear approximation to estimate Ay Ay =

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Q: Supose z is implicitly dofimed by the equation qy+ 3x + XyZ + 32=9 in an onvanment of the point…

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Q: Assume that after few w months, butterf lies papulace in looa is Calculated as: F(w)=12W+Cos (lbw)…

A: Minimum and maximum of a function can be calculated by testing the function against all the values…

Q: Let y= 3x2 +7x+4. If Δx=0.4 at x=2, use linear approximation to estimate ΔyΔy

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Q: 5. f'(x) dx = Choose... 6. cosh t dt = Choose...

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Q: Find the local linear approximation to f(x) = Vx at x = 1 and use it to approximate both 1.1 and…

A: To know which one is better we have to compare with calculator values of sqrt(1.1)  and sqrt(0.1)

Q: 18,8grt(10)) 10 f(x) = V2x – 2 compute the instantaneous slope at: (6, v10) Start with two points A:…

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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 output at a certain factory is Q(x, y) = 6x² + 3e36. ỹ+ 3y. %3D where x and y denote,…

A: The function is Qx, y=6x2+3ex36y+3y2. The marginal rate of substitution is given by dydx=-QxQy…

Q: Find the linear approximation of given function at (0, 0). 3x + 4 2y + 1 f (x, y) = f(x, y) =

A: We have to find the Linear approximation of the given function.

Q: suppose y = √(3x + 1), where x and y are both functions of t. If dx/dt = 2, find dy/dt when x=5

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Q: 5x? + 8x + 3. If Aæ 0.3 at x = 5, use linear approximation to estimate Ay Let y Ay =

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Q: Let y = sin(5x). If Ax = 0.4 at x = 0, use linear approximation to estimate Ay Δy ~ Find the…

A: Given: y=sin(5x) ∆x=0.4  at x=0   Solution: y=sin(5x) For the function y=f(x),   ∆y=f(x+∆x)-f(x)…

Q: The linear approximation at x and where B is:

A: Given a trigonometric functionf(x)=sin(6x)

Q: 7. Find the linear approximation near (2, 0) of f(x, y) = 3x e¯3ªy.

A: To find the linear approximation for the given function.

Q: Let y = 5x + 7x + 3. If Ax = 0.3 at x = 3, use linear approximation to estimate Ay Ay =

A: Follow 2nd step.

Q: The Technolozic Corporation has determined that its marginal cost function is given by C'(t) =…

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Q: A cylinder of radius r and height h has volume V = nr 2h.(a) Use the Linear Approximation to show…

A: Given: A cylinder of radius r and height h has volume V=πr2h a)  show:  ΔVV≈2Δrr+Δhhb)  Percentage…

Q: Suppose that t hours after the injection of x milligrams of adrenalin the response is R units, and…

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Q: 8. What is the relationship between a and b so that F(x, y) = (ary, 3ax + bry) is source free?

A: That's easy. Have a great day!!!

Q: the critical points, local e(s) and sat f(x, y) = 6x+4y+x² + y². Then find the maximum rate of…

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Q: Let y=2x^2+3x+3. If Δx=0.1 at x=4, use linear approximation to estimate Δy Δy≈

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Q: Using the linear approximation of f (x, y) near (x, y) = (1, 0) tells us that f (0.98, 0.05) is…

A: The linear approximation of a function f(x, y) at (a, b) is L(x, y) = f(a, b) + fx(a, b)(x − a) +…

Q: Find the linear approximation to the function f(x, y) = sin y --- |T at x, = (1, -2) 2 and use it to…

A: The solution is given as

Q: Y = 3x + 4x + 4. If Ax = 0.4 at x = 1, use linear approximation to estimate Ay Let Ay =

A: Given that                  y=3x2+4x+4    ...................(1)  and,    ∆x=0.4 Now derivative (1)…

Q: . On what interval is the curve y = . dt +t+ 2 concave downward?

A: For y to be concave downward, it's second derivative y''  < 0 We will use the Leibniz rule to…

Q: 18. Use the Linear Approximation to f(x, y) = /x/y at (9,4) to estimate 19.1/3.9.

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Q: 3- If the value of elasticity is equal to Ey = 0.21 then the ., note that 11.5 = xi = 10, yi %3D…

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Q: The output at a certain factory is Q(x, y) = 7x' + 4x/x e36 + 5y. where x and y denote,…

A: We’ll answer the first question since we answer only one question at a time. Please submit a new…

Q: Let y 3x + 4x + 4. If Ax = 0.4 at x = 1, use linear approximation to estimate Ay Ay =

A: Given, y=f(x)=3x2+4x+4 ,∆x=0.4 at x=1 Differentiate with respect to x, we get f'(x)=6x+4 At point…

Q: Fínd a differentiable curve y(x) that minimizes J = +

A: The objective is to find the differentiable curve yx that minimizes J=∫01y'x2+c2yx2dx if y0=0 and…

Q: The maximum rate of change of the function f (x, y, z) = x lIn(yz) at (1;2;-) is equal to: O 3 None…

A: We have to find the maximum rate of change of the function f(x,y,z)= x ln(yz) at (1,2,1/2).

Q: (8) Find the linear approximation of the function f(x) = Va at a = 25 and use it to approximate the…

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Q: The temperature in degrees centigrade (◦C) at each point (x, y) on a curve 2x + y = 3 is given by…

A: For relative maximum or minimum To maximize or minimize  a function f(x) 1st we need to find its…

Q: Consider the Cobb-Douglas production function f(x, y) = 100x1/3y2/3 where x is the number of units…

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Q: Find the interval on which the curve 1 dt 4+t+ 2t2 is concave upward.

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Q: 7 For the function eX, the linear approximation around x = 2 is %3D

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Q: Suppose that the marginal propensity to save is ds = 0.3 - dy (in billions of dollars) V 9y + 6 and…

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Q: Consider the Cobb-Douglas production function f(x, y) = 100x1/3y2/3 where x is the number of units…

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Q: Let y = 4a2 + 8x + 2. If Aæ 0.4 at x = 5, use linear approximation to estimate Ay %3D %3D Ay =

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Q: 12. If z = 2xy – 3x²y and x is increasing at 2 cm/s, determine at what rate y must be changing in…

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Q: Consider the function y defined implicitly by 3(x2 + y2)? = 100xy. Use the linear approximation at…

A: Given : 3(x² + y²) = 100xy

Q: What values of a and b make ƒ(x) = x3 + ax2 + bx have a local minimum at x = 4 and a point of…

A: Given: fx=x3+ax2+bx fx has a local minimum at x=4 . fx has a point inflection at x=1 . Since fx…

Q: Integrate from f(x) = x4 from 0 to 1 by (Trapezoidal Rule) with h = 1, h = 0.5, h = 0.25 and…

A: Here, f(x)=x⁴ So, I=  Integrate from f(x) = x⁴ from 0 to 1. Now we can solve by Trapezoidal rule,…

Q: Find the minimum and maximum of the function y = z – 1280z on [-5, 5] by comparing values at the…

A: The given function is

Q: Find the local linear approximation L (x)of the function f (x) = lnx at x = 1 %3D

A: LINEAR APPROXIMATION

Q: (1) Where on the line r = ay does the function f(r, y) = (x – a)² + (y – 2)² attain its smallest…

A: We need to check on the line x=ay.....................(1) if there exist a minimum for the function…

Q: Let y = 5x² + 4x + 4. If Ax = 0.3 at x = 4, use linear approximation to estimate Ay Ay ~ Submit…

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Q: Find the point where the maximum value of f(x, y) = xy subject to x + 5y = 74 occurs. (x, y, z) = |

A: