MATH 171 Midterm: Math 171 TAMU Fall 12 Exam1Solutions
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September 28, 2012: (15) state the de nitions of the following expressions/terms. (a) f (x) = lim x 1 . The vectors we"re seeking are projxxxyyy and yyy projxxxyyy. ||xxx||2xxx = yyy projxxxyyy = h2, 1, 1i . The vector projxxxyyy is parallel to xxx, and the second vector is perpendicular to xxx: (20) let f (x) = . 3 x, 1 x < 0. 1 x 2 x, (a) plot the graph of f . The limit does not exist at a = 1 and a = 0. Since the function is not de ned if |x| > 2, then technically the function does not have a limit at the endpoints of the interval [ 2, 2]. However, the limit from above exists at the endpoint 2, and the limit from below exists at the endpoint 2. (c) at what points a, 2 a 2, do one sided limits from above not exist.
