1. Consider the surface defined by z = x2 + e9y ln(x-y). Let f(x,y) =  x2 + e9y ln(x-y). ○ Compute ∇f at the point (1,0). ○ Compute the derivative of f(x,y) at the point (1,0) in the direction (3,-4). ○ Explain the geometric relationship between the answer found in part (a) and the surface defined above.

Q: 5. Find an equation plane to the surface (u, v) = (3 cos(u) sin(v), 2 sin(u) sin(v), cos(u)) at the…

A: First, we find the point on the surface where the tangent plane would be drawn. Next, we calculate…

Q: 6. Where does the tangent line to r = at the point (1, 0, 1) intersect the y-z plane.

A: Given:

Q: 2. Find the equation of the tangent plane to the surface x²+3y²+4z² = 20 (2,2, 1). at the point

A: Step 1:To find the equation of the tangent plane to the surface x2+3y2+4z2=20 at the point (2,2,1),…

Q: a) Determine the equation of the tangent plane of the graph of the function f(x, y) = 3x²y - 2y³ In…

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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: n exact form. Use symbolic notation and fractions where needed.)

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Q: 6. Find an equation of the tangent plane and a set of symmetric equations of the normal line to the…

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Q: Determine the equation of the tangent plane of the graph of the function f(x, y) = 3x²y-2y³ In the…

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Q: Find the equation of the plane tangent to the graph of z + xyz = 33 at (1,2,3).

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

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Q: Given a surface f(x,y) = -2x² + (5)y². Find the derivative in the direction of v = at the point (7,…

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Q: Find the equation of the tangent plane to the surface z = cos(6x) cos(3y) at the point (-2π/2,…

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Q: 1. The equation r²y³ +2ln(yz) + ye" - 1 determines a surface. Note that you cannot easily write z as…

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