Math 231 Fall 2017 Homework 7 Due Thursday October 12. Write clearly, and when possible, encase your final answer in a colored rectangle. Avoid using calculator, it won't be allowed in the tests (however, double checking your answers in the homework is not a bad idea). 1. Let : [0, ) R3 be the curve (t) = (cos t, sin t + t, e4t ). Determine the tangent line to the curve at the point (1, , e4 ). 2. Let : [0, loge (12)] R3 be the curve (t) = (t, et + et , 3t). Determine the length of . 3. Let : [0, 4] R3 be the curve (t) = (4t, 2 cos t + 6, 2 sin t). Parametrize by arc length and find its curvature at the point (4, 4, 0) . 1