11. [-/1 Points] DETAILS LARCALCET7 12.2.053.MI. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Find r(t) for the given conditions. r'(t) = 4e2ti + 7elj, r(0) = 2i r(t) = Need Help? Read It Watch It Master It6. [2/4 Points] DETAILS PREVIOUS ANSWERS LARCALCET7 12.2.023. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Find r'(t), r"(t), r'(t) . r"(t), and r'(t) x r"(t). r(t) = 2thi - 2ti + +3k 2 3 (a) r'(t) 5it + 272k - 2j (b) r"(t) 4kt + 5i (c) r'(t) . r" (t) (d) r'(t) x r"(t) Need Help? Read It7. [-/1 Points] DETAILS LARCALCET7 12.2.039. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Find the indefinite integral. (Use c for the constant of integration.) ( 2 ti + j + 4 k ) dt Need Help? Read It Watch It Viewing Saved Work Revert to Last Response 8. [-/1 Points] DETAILS LARCALCET7 12.2.040. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Find the indefinite integral. (Use c for the constant of integration.) ( 4 1 31 + 10 ] - 9 v th ) at Need Help? Read It Submit Answer 9. [-/1 Points] DETAILS LARCALCET7 12.2.048. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Evaluate the definite integral. Need Help? Read It 10. [-/1 Points] DETAILS LARCALCET7 12.2.052. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Evaluate the definite integral. Need Help? Read It Watch It1. [-/4 Points] DETAILS LARCALCET7 12.2.004. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Find r'(t), r(to), and r'(to) for the given value of to. (t) = (5 + t)i + tsj, to = 1 r'(t) = r(to) : r'(to ) = Sketch the curve represented by the vector-valued function, and sketch the vectors r(to) and r'(to). 00 (1, 6) 4 (0, 5) 2 L -2 -1 2 -2 -4 X (0, -5) (1, -4) 1 2 O w 4 r' 2 2 (-4, 1) (6, 1) r 'X -6 -4 -2 2 A 6 (-5, 0) (5, 0) O - 1 O Need Help? Read It\f4. [2/3 Points] DETAILS PREVIOUS ANSWERS LARCALCET7 12.2.020. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Find the following for the given equation. r (t ) = (+2 + 8t )i + (+2 - 8t)j (a) r'(t) = i(2t + 8) + 2jt - 8j V (b) r"(t) = 2j + 2i (c) Find r'(t) . r"(t). Need Help? Read It 5. [2/3 Points] DETAILS PREVIOUS ANSWERS LARCALCET7 12.2.021. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Find the following for the given equation. r(t) = 5 cos(t)i + 5 sin(t)j (a) r'(t) = 15(-sin (t) ) + j(5 cos(t) ) ( b ) r" ( t ) = -5i cos ( t) - 5j sin (t) V (c) Find r'(t) . r"(t). X Need Help? Read It Watch It2. [-/4 Points] DETAILS LARCALCET7 12.2.010. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Find r'(t), r(to), and r'(to) for the given value of to. Then sketch the space curve represented by the vector- valued function, and sketch the vectors r(to) and r'(to). r(t ) = ti + taj + =k, to = 2 "'(t) = r(to ) = r' (to ) = - Z 2 6 r' O O 2 -4 - 2 -24-21 2 O O Need Help? Read It2. [I3 Points] DETAILS LARCALCET7 11.2.051. MY NOTES ASK YOUR TEACHER Find the component form and magnitude of the vector v with the given initial and terminal points. Then nd a unit vector in the direction of v. Initial point: (4, 6, 0) Terminal point: (4, 1, 8)