Practice probleus #16. Math 2043, Fall 2017 1 Let F(r.) be the vector field defined by the formala F(z, y) = (yeon(ry)-sin(z + y), zoon(ry)-sin(z + y)). Compate for each of the following curves: (1) ?(t) = (t,t2), t ⬠10, 11 (3) n0)-(.t, 10,1 and plot each of the e Recall that ds dt 2. Let y,), let curves. (All three are easy to evaluate using substitutions) lt)-(3(1-1),-2(1 t) te o,1 Plot the curves 2 and evaluate the line integrals F-ds. 3. Let P(, v), Q(a, y) be the conponeuts of the vector field in Problem 1. Compute and explain why the value you obtained for the difference implies that the answers to the line integrals in Problem 1 are all the same. 4ãLet A = ( 1.2), let B = (3,1). Parametrize the line segment from A to B of the line segment from A to B can be obtained by Example. A letting a and &be the position vectors for the points A and B and using the formala Note that γ(0)-E(_ A) and '(1)-6(_ B) and if t is between 0 and 1, then "(t) is a point on the line through A. B and lies between these two points. For example, if A (2,5) and B-(1,3), then æ°´)-(2.5) + t((1,3)-(2.5)) -(2-t,5-21) Exercise: Evaluate t) for t each o 0, 1/4. 1/2,3/2, 1 and plot the resulting points 5·Let T be triangle with vertices A = (1,0), B = (3,0). C= (3,2)ãLet F(z, y) = P(z, y)T+ Q(z, y). with Evaluate Or y directly (without using Green's Theorem).
