5. Let f(x, y) = xln(x/y)+ xy² a. Calculate f and fx b. Determine the directional derivative off at the point (2, 2) in the direction of the vector a=i-2j c. Suppose that x = ste' and y=2se¹. Calculate af Ət d. Determine an equation for the tangent plane to the surface z = f(x, y) at the point (2, 2, 8) on the surface.

Q: 6. Find the unit vectors that are parallel to the tangent line to the curve 2x3 at the point (2,…

A: The given curve is y=2x33 at the point 2,163. Calculate the unit vector that are parallel tot he…

Q: Calculate directional derivatives and gradients in three dimensions. Find an equation for the…

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Q: 3. Let f(x, y) = xy+ y². Find the equation of the tangent line in parametric form in the x-direction…

A: Solve the following

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: 6. Given f(x, y) = 2x³y=x²y³, a) find the directional derivative of f(x, y) at (1, 1) in the…

A:

Q: 6. Let F(x, y, z)=2xy² + 2yz² + 2x²z. a. Determine the maximum directional derivative of F at the…

A:

Q: 2) Sketch the curve with the vector equation r(t) = costi- costj+ sin tk. Show the direction of…

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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: 3xyz = 63 and 3x² + 4y² + 8z² = 423 at point (−3, 1, −7). ř(t) = with -∞ < t <∞

A: The parametric form of a line that passes through x0, y0, z0 and has the direction ratios: a, b, c…