(Solution) - a Use Exercise 81 to show that the angle between the -(2025 Original AI-Free Solution)

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(a) Use Exercise 81 to show that the angle between the tangent line and the radial line is ? = ?/4 at every point on the curve r = e6.
(b) Illustrate part (a) by graphing the curve and the tangent lines at the points where ? = 0 and ?/2.
(c) Prove that any polar curve r = f (?) with the property that the angle ? between the radial line and the tangent line is a constant must be of the form r = Cek6, where C and are constants.