1. [-/2 Points] DETAILS LARCALCET7 15.2.010. MY NOTES ASK YOUR TEACHER Consider the following. C: line segment from (0, 0) to (4, 8) (a) Find a parametrization of the path C. r (t ) = Ost s 4 (b) Evaluate (x2 + y2) as. 2. [-/1 Points] DETAILS LARCALCET7 15.2.021. MY NOTES ASK YOUR TEACHER Evaluate the line integral along the given path. 1 ( * 2 + 4 2 + 2 2 ) ds C: r(t) = sin(t)i + cos(t)j + 5k osts . 3. [-/1 Points] DETAILS LARCALCET7 15.2.024. MY NOTES ASK YOUR TEACHER Find the total mass of two turns of a spring with density p in the shape of the circular helix below. r(t) = 4cos(t)i + 4sin(t)j + 8tk p ( x, y, Z ) = z 4. [-/1 Points] DETAILS LARCALCET7 15.2.029. MY NOTES ASK YOUR TEACHER Evaluate F . dr. F(x, y) = xi + yj C: r(t) = (9t + 1)i + ti, osts15. [-/1 Points] DETAILS LARCALCET7 15.2.037.MI. MY NOTES ASK YOUR TEACHER Find the work done by the force field F on a particle moving along the given path. F(x, y) = xi + 4yj C: x = t, y = t> from (0, 0) to (2, 8) 10 8 6 4 2 6 8 10 6. [-/1 Points] DETAILS LARCALCET7 15.2.056. MY NOTES ASK YOUR TEACHER Evaluate the line integral along the path C given by x = 2t, y = 6t, where 0 s t s 1. ( y - x ) dx + 5 x 2 * 2 dy 7. [-/1 Points] DETAILS LARCALCET7 15.2.057. MY NOTES ASK YOUR TEACHER Evaluate ( 2 x - y ) dx + ( * + 7 y ) dy . C: x-axis from x = 0 to x = 48. [-/4 Points] DETAILS LARCALCET7 15.2.015. MY NOTES ASK YOUR TEACHER Consider the following. C: counterclockwise around the triangle with vertices (0, 0), (1, 0), and (0, 1), starting at (0, 0) (a) Find a piecewise smooth parametrization of the path C. Osts1 r(t) = ists 2 2sts 3 (b) Evaluate ( * + 7Vy ) ds. 9. [-/2 Points] DETAILS LARCALCET7 15.1.037. MY NOTES ASK YOUR TEACHER Determine whether the vector field is conservative. F (x, y) = (7y - x2)i + (7x + y)j conservative not conservative If it is, find a potential function for the vector field. (If an answer does not exist, enter DNE.) f ( x , y ) = + k 10. [-/1 Points] DETAILS LARCALCET7 15.1.060.MI. MY NOTES ASK YOUR TEACHER Find the divergence of the vector field F. F ( x , y , z ) = In( 9x2 + 8y2 )i + 72xyj + In(8y2 + 522)k div F ( x , y , Z ) = 11. [-/5 Points] DETAILS LARCALCET7 15.1.046.MI. MY NOTES ASK YOUR TEACHER Find the curl of the vector field at the given point. F (x, y, z) = x2zi - 2xzj + yzk; (5, -9, 5) curl F =