| Let ƒ(x, y) = 4x² + 7xy + 4y² + 7x − 7y + 4. Find the linearization L(x, y) of f(x, y) at the point (-1,2). L(x, y) = Find an upper bound for the magnitude |E| of the error in the approximation f(x, y) ≈ L(x, y) over the rectangle |x + 1| ≤ 0.2, ly - 2| ≤ 0.2. |E| ≤ 899 =

Q: 7. If V=set of integers ending with 3; then V is O C a. A vector space under addition multiplication…

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Q: Q2) a) Find Maclaurin expression of f (x) = Cosh (x) b)Find the gradient of the function f(x, y, z)…

A: Part (a) General form of function fx is Maclaurin series is…

Q: m and n, mn, such that: and U(m) ~U(n). Find integers a) |U(m)| = |U(n) b) |U (m)| = |U(n) and U(m)…

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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: Use the gradient to find the directional derivative of the function at P in the direction of Q. f(x,…

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Q: a) Find the directional derivative of the function f(x, y, z)= x² y2 (2z+1)2 at the point P:(1, - 1,…

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Q: Let f: R² → R be a differentiable function. (a) At the point (ro. Yo) = (1,5), it is known that the…

A: Given That : Equation of tangent plane to the surface z=fx , y is -2x+3y-z=17. To Find : a)…

Q: Find the number of zeros of f(z) = z' + iz² – z + 2i in the upper half-plane.

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Q: Find (url and dive rgence the of F(xy2)=Xy2 i+ 2x Y j t z(os xyk.

A: Given: F(x, y, z) = xyz i + 2xy j + 2cosxy k To find: Curl and divergence of the given function.

Q: d) Consider the fourth-order truncation error (0(Ax )4) with the step size Ax and also (-Ax) then,…

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Q: Determine the two-variable function F(x, y) if Fy (x, y) = y sin(xy) + x given that x-² F(x₁ - ²) =…

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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: SF. dr, where F (x, y) = (6x − 2y)i +x²7, Evaluate from (6,-3) to (0, 0). and C is the line segment

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Q: Find the derivative of the function f (, y, z) = 4ay z at the point (4, 64, 16) in the direction of…

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Q: Compute F · dr where F(x, y) = and C is the path traced by the line segment starting at (0, −1) and…

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

A: The truncation error is of order O∆x3 The step length are ∆x, -∆x

Q: a) Find the derivative of f(x, y, z) = 4zx – xy² – z,at P,(1,0, 2) in the direction of v = 4i – 5j +…

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Q: The derivative of ƒ(x, y) at P0(1, 2) in the direction of i + j is 2sqrt(2) and in the direction of…

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Q: The graph of y=x'-3x-24x +32 is concave upward on the interval (1, oo) because: O'=y"=0 Oy' is…

A: The given function is y=x3-3x2-24x+32