Question: 1. Consider the curves C and C parametrizationd r - sin 2t, y - cos 2t, respectively, for 0 I. Consider the curve; Cl and

1. Consider the curves C and C parametrizationd r - sin 2t, y - cos 2t, respectively, for 0

I. Consider the curve; Cl and CQ parametrized by r t, y Sint, and sin y cos2t, respectively, for O t 2K. Draw thc graphs of and and indicate all values of t in [O, 2111, if any, for which C', (t) C2(t). 2. (a) Undex what conditions is it possible to rx-nsider a parametrized curve. as the graph of a function? (Hint: If f (t) and y g(t) for t b, what might one let f(t) be?) (b) Write down parametric equations for a general line L (c) We, are given a differentiable function f on [a, whose, graph is C. Derive thc formula for thc length L of C' from the formula for the length of C' when f is given parametrically.

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