Let f: C C be defined by f(z) = z² and let L₁ be a line parallel to the x-axis and L₂ b another line parallel to the y-axis. 1. Find the curves into which L₁ and L2 are transformed by f. 2. Do the transformed curves meet at right angles? Why do these curves meet twice?

Find Av, where v = (3,5). 0 -1 A = -1 Av = Describe the transformation. The transformation is a reflection over the y-axis. The transformation is a horizontal stretch. The transformation is a reflection over the line y = x. The transformation is a vertical stretch. The transformation is a reflection over the line y = -x. The transformation is a reflection over the x-axis.

Example 3.1. Consider the curve x = 4(3+y). Compute the length of it when 1 ≤ y ≤4.

1. Let the line L be defined by x=t+1 y = 2t +12=3t+1 (a) Write a formula for the distance between the point (1,1,0) and an arbitrary point on the line L. (b) Farmer Bob was walking near a golf course when a golf ball comes whizzing by. Suppose the golf ball is following the line L (with units measured in inches) and t is measuring how many minutes since the golfer swung at the ball. Find out how close the ball came to hitting Farmer Bob, and at what time t that happened. 2. Let the surface S be defined by x² + y² +2²+2x2 = 1 (a) Plug in the values z = 0, z = 1. What is the graph of the resulting equation? (b) Plug in the values y = 0, y = 1. What is the graph of the resulting equation? (c) Plug in the values z = 0, z = 1. What is the graph of the resulting equation? (d) Describe what the surface looks like. Attempt to draw it (preferably using your answers from a,b and c).

25. Consider the curve defined by the equation below and a point (2, 1) on the curve. What is the equation of the tangent line at the point (2, 1)? x? - 3y = 1 4х — Зу- 5 %3D 0 4x – 3y + 2 = 0 2х — 3у - 1 %3 0 4х — 3у + 5 %3 0 |

Let F = (2y, 7x, 22). CA C₁ C₂ C₁ Choose the statement(s) about the curves given in the figure that are always correct. OqFdr = JF. dr OqFdr = JF. dr SqF. dr = √3F.dr OfF.dr = fF.dr OF. dr = F. dr OqFdr = √F.dr