H. Use the gradient to find the equation of the tangent plane to each of the surfaces at the given point. a) x² + 3x²y-z = 0 at (1,1,4) (Answ: 9x+3y-z = 8) b) z = f(x, y, z) = r²y³z at (2,1,3) (Answ: 4x - 3y -z = 2) I. In electrostatics the force (F) of attraction between two particles of opposite charge is given by (Coulomb's law) where k is a constant and r = (x, y, z). Show that F is the gradient T (Hint: ||||||(x, y, z)||). Important problem! F(r) = k₁ of P(7) ||7-1³ -k ||1| =

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: Suppose ƒ(1, 2) = 4, ƒx(1, 2) = 5, and ƒy(1, 2) = -3. Find an equation of the plane tangent to the…

A: Equation of the plane tangent to the surface  z=f(x, y) at (a, b) is z=fa, b+fxa, b(x-a)+fya, b(y-b)

Q: Find an equation for the tangent plane to the surface 2? – ry? = 0 at the point G, 2, 3)

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Q: 7x + 3y xy+1 (a) Compute Vf at the point (2,-4). 1. Let f(x, y) = (b) Compute the derivative of f(x,…

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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: tangent plane

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Q: The temperature at the point (x, y) on a metal plate is given by T (x, y) = y/(x2 + y2 ). Find the…

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Q: Find an equation for the tangent plane to the surface x = u² – v², y = u + v, 2 = u² + 4v at (-},2).

A: We have r(u,v) = (u2-v2)i + (u+v)j + (u2+4v)k