A Boeing 747 jumbo jet maintains a constant airspeed of 550 miles per hour (mi/hr) headed due north. The jet stream is 100 mi/hr in the northeasterly direction. (a) Express the velocity va of the 747 relative to the air and the velocity vw of the jet stream in terms of i and j. (b) Find the velocity of the 747 relative to the ground. (c) Find the actual speed and direction of the 747 relative to the ground.

Lecture 8: Evaluating Limits (Sections 2.3 and 2.5) Basic Limit Laws Suppose x→c f(x)adml x→c g(x)xtnd k is a constant. We have the following limit laws: 1. x→c [f(x) ± g(x)]= 2. lim kf (x)= x→c 3. lim f(x)g(x)= x→c 4. If lim g(x) ,l0 f(x) = x→c x→c g(x) 5. If p, q are integers, with q enl,t [f(x)]p/q= x→c Assume that lim f(x) ≥ 0fi q is even, and that x→c lim f(x) ▯=if p/q < 0. x→c In particular, for a positive integer n: n ▯n lim [f(x)] = , lim f(x)= x→c x→c