A curve is described by ~r(t) = het sin t; et cos t; 0i. Its graph over the inte

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A curve is described by ~r(t) = het sin t; et cos t; 0i. Its graph over the interval 0  t  3 2 is shown below along with points spiraling out from (0; 0) plotted for t values of 0; =3; 2=3;  and 4=3. 1. Find the arclength function s(t) where we measure the curve starting from the origin at t = 0. Use the arclength function to find the length of the curve graphed above (0  t  3=2). 2. Solve the arclength function for t in terms of s and use this formula to parameterize ~r in terms of the arclength s; i.e. find ~r(s). 3. Using the result from the previous problem, find the coordinates of the point, accurate to nearest 0.1, at a distance of 120 along the curve from the origin. 4. Find the curvature (t). 5. Use the relation between t and s from part (2) to parameterize  in terms of s; i.e. find (s). From this result find the values of (0) and (5), the curvature at the origin and at the point five units along the curve from the origin, respectively

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