3. Let C be the curve with parametrization given by r(t) = (t − 1)i +3t²j + tk for t € R. The tangent line to C at the point (0,3,1) intersects the xy-plane at the point A. (1,9,0) B. (-1,0,0) C. (-1,-3,0) D. (3,3,0) E. (1,-9,0)

Q: 3. Use implicit differentiation to find əz - for ?х x²+2y²+5z²=2.

A:

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A: Solve the following

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A: We use line integration to evaluate this.

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

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A: This is problem of vector calculus.

Q: П π Find T, N, and k for the plane curve r(t) = 7t i +7 In (cost) j. - <t<2.

A: Since you have uploaded multiple questions according to our guidelines we have solved first question…

Q: 2. Find a set of parametric equations for the tangent line to the curve of intersection of the…

A: Step 1:To find the parametric equations for the tangent line to the curve of intersection of the…