8. Find the curvature at a general point on each of the following curves. (Hint: First...

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8. Find the curvature at a general point on each of the following curves. (Hint: First find u, then du. Then k = dud since this expression is equal to |du|/ds = |du|.) dt dt a+bt (a, b constant) dt (b) r = a(cost, sint) (a constant) (a) r = (c) r = (t, t) (d) r = (t, cosh t) (e) r = (2t sin 2t, 1 cos 2t) (cycloid) (f) z r = (cost, In(sect+tant) sint) (h) r = ae (1- it)eit for t> 0 (see Question 5) ae (use Question 3). 8. Find the curvature at a general point on each of the following curves. (Hint: First find u, then du. Then k = dud since this expression is equal to |du|/ds = |du|.) dt dt a+bt (a, b constant) dt (b) r = a(cost, sint) (a constant) (a) r = (c) r = (t, t) (d) r = (t, cosh t) (e) r = (2t sin 2t, 1 cos 2t) (cycloid) (f) z r = (cost, In(sect+tant) sint) (h) r = ae (1- it)eit for t> 0 (see Question 5) ae (use Question 3).