MATH 241 Lecture 19: Lecture 19 - Vector Fields on Curves and Conservative Vector Fields

1. (1+2-3pts) Determine whether the following vector fields F are conservative on R2 and R, respectively. Explain why. (a) F = (ln y + 2r + y2, _ +13) (b) F = (2m + y2, 2xy, x2 + 3H)

M273(Multivariable Calculus) Mini Quiz B Fall 2017 (Sec 02) Maximum points 13 Due Nov 27, Monday, 1:00pm Show all your work. No poins l be given for only providing the answers with no work, or even for correct answers with incorrect work. Circle your final answer Name: 1. (1 +2=3pts) Determine whether the following vector fields F are conservative on R2 and R, respectively. Explain why (a) F = (In y + 2z + y, z + zy)

Problem 5, Calculate the volume of the solid bounded by the cylinder z = 2 and the planes 2-a, y-0, y -2 Field lines, conservative fields Problem 6. Find the field lines of the vector field F = (1,s). Show that F is conservative and find its potential. Draw the field lines and the equipotential lines on the same coordinate system