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151review2solF09

151review2solF09 - Partial solutions to the Math 151 review...

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Partial solutions to the Math 151 review problems for Exam 2 These are not complete solutions. They are only intended as a way to check your work. (1) The limit is - 4. The L’Hˆ opital Rule is much more efficient than using long division to factor ( x - 1) 2 out of the numerator and denominator. (2) The L’Hˆ opital Rule gives 1 / 3. In Math 152 you will learn a more efficient way to find this limit. (3) The horizontal asymptotes are y = 1 7 and y = - 1 7 . (4) All of your answers except horizontal asymptotes can be checked using your graphing calculator and a viewing window with - 4 x 4 and - 4 y 4. The horizontal asymptote for (a) is y = 1. The horizontal asymptote for (b) is y = 0. (5) The critical points are x = ± 1 and x = ± 2 / 5. The inflection points are x = 0 and x = ± 3 / 10. If you use your graphing calculator to check the remaining answers, then you will have to choose the graphing window carefully to see confirmation of the following: The function is decreasing on ( - 1 , - 2 / 5) and (2 / 5 , 1). This is not obvious if the viewing window is - 2 x 2, - 4 y 4, for example.
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