MATH 3C-L3 - EXAM #1 Laney College, Spring 2023 Fred Bourgoin Give exact answers whenever possible. Do not skip steps. Carefully justify your answers for full credit. Good luck! 1. Sketch a contour diagram for f(r, y) = vi + y with at least four level curves. 2. Consider the following values of some function f(r, y). (a) Could f be a linear function? Justify your answer. (b) If you answered "yes" to (a), find an expression for f(r, y). If you answered "no" to part (a), you did it wrong. 3. Given # = (1, -3,2), # = (-1, 1, 1), w = (2,0, 1), compute the following. (a) 37 - 21 (d) J.W (b) |7+ will (e) proja () (c) 171 + 1 1 (f) The angle between if and uf 4. Find an equation for the plane perpendicular to # = (3, -2, 4) and through the point P = (1, 1, -1). 5. Find a unit vector perpendicular to u = (1, -3,2) and # = (-1, 1, 1). 6. Find the area of the triangle with vertices P = (4,3, 1), Q = (1,1, -1), and R = (0, -2, 1). 7. Find a possible equation for the linear function with the given contour diagram. 8. Sketch the graph of f(x,y) = y