8. Given the space curve r(t) = (sin²t, cos't, tant), find an equation of the tangent line in parametric form to this curve when t ==. 4

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A: Given that,

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A: To solve Differential equation.

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A: We can solve the given problem by using the concept of derivatives.

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A: Given that,

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A: Derivate the given equation with respect to x.

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A: See this  solution in below

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A: To find out the solution of the differential equation.

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A: Solution is given below:

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A: Please see the below picture for detailed solution.

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Q: Compute the double integral ff(6zy2 +12z³y + 4y) dx dy with R= 3,5 z [1,2].

A: See this solution in below.

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A: Calculating determinant of a matrix is the key requirement for this problem.

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A: We have to solve given integration by partial fraction decomposition.