7 → V by a(f)(x) = x² ƒ"(x), where ƒ" (x) is the double differential of a polynomial f(x). pjection? re exist a subspace WCV of V such that V = Im(a) + W?

Q: Question 4 Find the gradient of the function at the given point. w = 2x - 4yz+z², (1, 1, −2) 21+…

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Q: Let F(x,y,z) = (x)i + (y)j + (z2)k. Compute the defined operations and if it is not defined, write…

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Q: ind positive constants b and n, such that 3n + 2 n.

A: Finding the values of b and no

Q: of the form y₁ = (1+₁2+ a₂x² + 3x³ + ...) 32 = x2(1+b₁x + b₂x² + b₂x³ + ...) where T₁ > T2- Enter…

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Q: Suppose f(x, y, z) = xyz + 2xy + 2² · Compute the following values -(2,8₁16) - (-2,-8, 16) (1,-1,0)…

A: We have to find functional value.

Q: = 0. c) y(0) = 1, y'(0) = 0, y"(0) = -1. Is the set of functions linearly independent or linearly…

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Q: -3t k Compute the first, second, and third derivatives of r(t) = 3ti + 5 In(t)j + 5e

A: r(t)=(3t)i+(5lnt)j+(5e-3t)k   We are required to findFirst derivative Second derivativeThird…

Q: Let f(x,y) = x - 4xy - y. Compute f(4,0) and f(4, – 4). f(4,0) = (Simplify your answer.)

A:

Q: f (x, y) ~ bo + b1,0(x − 1)+b0,1(y−2)+ b2,0 (x - 1)² + b₁,1(x − 1)(y-2) + bo,2(y − 2)² +…...

A: We find the Taylor series of the given function