Question 2(b): Study the curve you plotted in part 2(a) by rotating the view. Th

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Question 2(b): Study the curve you plotted in part 2(a) by rotating the view. The appearance of this graph is due to the fact that this vector function lies on a sphere. The equation of a sphere with radius 1 is X^2 + y^2 + z^2 = 1. By substituting the expressions for x, y and z above into the equation of the sphere, show that this vector-valued function lies on the sphere's surface. (Do this verification by hand in the space below-i.e., show that the right-hand side of the equation is equal to the left-hand side of the equation after substitution.) Question 3: Plotting the Tangent Line to a Space Curve IMPORTANT: Do this question after you have completed tomorrow's lecture on Derivatives of Vector-Valued Functions. Consider the curve with the following parametric equations: x = 2 cos(t) y = 2 sin(t) z = 4 cos(2t) Question 3(a): Find the parametric equations for the tangent line to this vector-valued function at the point (root 3, 1, 2). Do this part by hand calculation. Show all of your work in the space provided. Question 3(b): Using Maple's spacecurve and display commands, graph the curve of this vector function together with the tangent line at (root 3, 1, 2). Use the parameter domain t = -Pi ..Pi for the plot. Rotate the plot of the curves to achieve the best viewpoint that illustrates the location of the tangent line before you print.

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