1. Given f(x,y) = 2x² + y² whose graph is a paraboloid. Fill in the table with the values of the directional derivative at the points (a,b) in the directions given by the unit vectors, u, v and w. |(a, b) = (1, 0) (a, b) = (1, 1)| (a, b) = (1, 2) u= (1, 0) (V₂². V²) 2 (0, 1) Interpret each of the directional derivatives computed in the table at point (1,0) V = 2=2x² +

Q: 5. Find the directional derivative of f(x, y) = xy – y at the point (1, 2) along the unit vector…

A: The given function is: f(x,y)=xy-y2 Given point is: P = (1, 2) Direction vector is: v=3, 4

Q: 6. (a) Find the directional derivative of w = x²y² at the point (1, -3) in the direc- 5T 5T tion of…

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Q: Let f(x, y) = 10-3r² +4. (a) Find the gradient Vƒ(2,-3) of f at the point P(2,−3). (b) Find the…

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Q: Suppose that f(z,y) is differentiable, and suppose that the directional derivative of f at the…

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Q: Suppose we know that for a function f we have Vf(x, y) = (6x, 6). Find the directional derivative of…

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Q: Suppose ƒ is differentiable at (9, 9), ∇ƒ(9, 9) = ⟨3, 1⟩, and w = (1, -1). Compute the directional…

A: Given that ∇ƒ(9, 9) = ⟨3, 1⟩. Note that w = (1, -1) is not a unit vector. Its unit vector along same…

Q: The vector function r(t)-(26)j + (46² +116) k is parallel to its derivative r(t)- dr/dt when t…

A: We have to find the value of t for which vector function r(t) is parallel to r'(t).If two vectors…

Q: c) Find the directional derivative of f(x,y) = 10 – 3x2 + at P(2,–3) in the direction of the vector…

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Q: Use a FULL truth table to determine whether the given argument form is valid or invalid. Write a…

A: ANSWER

Q: Suppose z is implicitly given by the equation x³y-yz²+ -5 x In a neighborhood of the point P(1, 1),…

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Q: Suppose that over a certain region of space the electrical potential V is given by the following…

A: Given that, Vx,y,z=4x2-3xy+xyz Find Vx,Vy,Vz:  Vx=8x-3y+yzVy=-3x+xzVz=xy Gradient of V at P(6,6,5)…

Q: Find the directional derivative of the function at the given point in the direction of the vector v.…

A: Here we use the formula, Dvf(x,y)=∇f(x,y).v

Q: rative of the f he unit vecto p, then Ja + B|

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Q: Let n  ∈ Z with n>0. Prove that n | (n+1)n  - 1.

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Q: 2. [-/16.66 Points] DETAILS Find the directional derivative of the function at the given point in…

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