Let a > 0 and let f: [0, a] –→ R be an increasing continuous function. Consider the curve C parametrized by cos(f(x)) dr, sin(F (2)) da a) Show that C is parametrized by arc length. b) Determine the...

Extracted text: Let a > 0 and let f: [0, a] –→ R be an increasing continuous function. Consider the curve C parametrized by cos(f(x)) dr, sin(F (2)) da a) Show that C is parametrized by arc length. b) Determine the curvature k(s) of C. c) Use b) to find a parametrization of the curve whose curvature is given by K(s) = s, with s > 0.