'ind parametrizations (a) The line from (a, b) to (c,d). (b) A path from (2,0) to (0, −2) along a circle of radius 2 the “short way" around. (c) The intersection of x + 2y + 3z 6 and x² + y² = 9. for the following curves. Don't forget to give the bounds on t. =

Let F(x, y) = (x + 1)j, and let C be the portion of the parabola y starts at (0,0) and ends at (2,4). x² that Y 4 (a) Without doing any calculations, state whether f F. ative, or zero. diagram to the right how you know your answer is correct. • dr is positive, neg- Clearly state your answer, and explain based on the 2 (b) Calculate So F •dr. Clearly show all of your work, including your setup and calculation of the integral, and circle your final answer.

(ii) Make a contour plot of the function z(x, y) = -xy in the xy-plane, by drawing a collection of curves z(x, y) = c for different (positive and negative) values of the constant c. Try and sketch a graph of the function in the space of xyz coordinates (as a check you may want to compare that sketch with a computer/Python graph).