Determine a unit vector u = (a, b) with positive a such that at the point (x, y) = (1,1), the directional derivative of T in the direction of u is zero The gradient vector VT (x, y) always points in a direction perpendicular to the curve x² + 2y² = 5. True False The temperature T at a point (x, y) is given by the function 1 T (x, y) = x²+2y²+1 At the point (x, y) = (1, 1), what is the rate of change of T traveling in the direction aligned with the vector (1, 2). If your

Q: 5. Find the directional derivative of f(x, y) = y² + (x²/y), at the point (2, 1) in the direction of…

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Q: f(x,y,z)=5sin(xyz), (a,b,c)=(1,1,π/4), and v⃗ =(3,-√2,3). Calculate the directional derivative…

A: Here we will evaluate each expression.

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

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Q: Find the directional derivative of the function f(x, y) = ln(x³ + y³) at the point (3, − 2) in the…

A: Use the gradient of function for finding the directional derivative.

Q: 2. Consider the function f(x, y) = a) Find the directional derivative of f in the direction of the…

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Q: Find the directional derivative of the function f(x, y) = In(x +y°) at the point (2, 3) in the…

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