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6. Consider the vector value function r(t) = 4 root t+2 ii + In(3 - t)j + t^2 k. a. Determine the domain of this function. b. Find the limit: lim t tends to 2 r(t) c. Determine r'(t) and r'(2). 7. Let r(t) = (t - 1)i+ t^2j + e^-tk. a. Find the indefinite integral integrate r(t)dt. b. Determine the definite integral integrate limit 0 to 2 r(t)dt 8. (Extra Credit) Determine the length of the curve: 9. Let F1 and F2 be the two forces shown below, with |F1| = 10 lb, and |F2| = 12 lb. Determine the magnitude and the direction of the sum of these forces F1 + F2.
Show transcribed image text 6. Consider the vector value function r(t) = 4 root t+2 ii + In(3 - t)j + t^2 k. a. Determine the domain of this function. b. Find the limit: lim t tends to 2 r(t) c. Determine r'(t) and r'(2). 7. Let r(t) = (t - 1)i+ t^2j + e^-tk. a. Find the indefinite integral integrate r(t)dt. b. Determine the definite integral integrate limit 0 to 2 r(t)dt 8. (Extra Credit) Determine the length of the curve: 9. Let F1 and F2 be the two forces shown below, with |F1| = 10 lb, and |F2| = 12 lb. Determine the magnitude and the direction of the sum of these forces F1 + F2.