MATH 151 Midterm: MATH 151 TAMU Y2011 2011a Exam 2b Solutions
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Exam ii version b solutions: e di erentiate to nd the velocity: s (t) = 6t2 42t + 72, so s (1) = 36. you limit: d if key jugate: don"t just multiply remember by the con- 2x(1 + cos x) sin x x sin x. 1 f (g(2): a g (2) = f (x) = 3x2 + 1. Then 2 = f (y) = y3 + y. By inspection, y3 + y = 2 when y = 1. 4: b g (x) = xf (x) + f (x)(1), so m = g (2) = Di erentiate, substi- tute, and solve: y = rerx, y = r2erx. Then r2erx + rerx 6erx = 0. erx(r2 + r 6) = erx(r + 3)(r 2) = 0. Since erx 6= 0, r = 3 and r = 2. The solutions are y = e 3x and y = e2x, which means none of these is cor- rect: c at the exponent.
