For each of the following vector fields F , decide whether it is conservative or not by computing the appropriate first order partial derivatives. Type in a potential function f (that is, Vf = F) with f(0, 0) = 0. If it is not conservative, type N. А. F (х, у) — (-10х — 5у) і + (-5х + 10y) j f (x, y) = В. F (х, у) — -5yi — 4аj f (x, y) = С. F (г, у) — (-5 sin y) i + (—10у — 5ӕ cos y) j f (x, y) =

Q: 3. Calculate the directional derivative of the function f : R³ → R, defined by f(x, y, z) = y²+xz at…

A: Step 1: Step 2: Step 3: Step 4:

Q: Find the derivative of the vector function 7(t) = (e²¹, e-3¹, t). Find an equation of the line…

A:

Q: (a) Find the direction for which the directional derivative of the function f(x, y, z) = √√x² + y² +…

A:

Q: 2.31 Let A and B be vector functions of position vector x with continuous first and second…

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Q: Let r(t)= Determine the interval(s) on which this vector valued function is continuous.

A:

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A: Given that: drdt=<e-t, 3e3t, -2t>          and r(0)=2i-j+k

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A: Given,f(x,y,z)=xyz     As we know ∇f(x,y,z)=∂f∂x,∂f∂y,∂f∂z

Q: 3 - Find the Derivatives of the following Vectors, Where F(t)* = 2secti – 3j* + csctk and G(t)* =…

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Q: (I) The directional derivative Duf(a, b) is parallel to the vector u. (II) If u is perpendicular to…

A:

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Q: Why is r(t) = ⟨ƒ(t), g(t), h(t)⟩ called a vector-valued function?

A: Given r(t) = ⟨ƒ(t), g(t), h(t)⟩. We need to give reason why r(t) is called vector-valued function.