Question 1:

Let r(t) : (sin 75, 2 cos t, it) parameterize a curve C in R3. (a) Sketch the curve C over 0 g t g 7r. (b) Find the normal and tangential components of acceleration as functions of parameter t. Determine the normal and tangential components of acceleration at times 20,152 gandtzw. (b) Determine the curvature of the curve C as a function of parameter t, that is find 5(25). Determine the curvature at t : 0,15 : g and t : 7r. Consider the function r(t) 2 (ct cos 2t, 8t Sin 2t1 at) which parameterizes a curve C in R3. (a) Find r'(t) and r\"(t). (b) Give a parametric equation for the tangent line to the curve C at the point r(t : 0). (c) Find the length of the curve C over 0 g t g 37r