Exam_I_Solutions

# Exam_I_Solutions - M ATH 115 F IRST M IDTERM E XAM N AME I...

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2 1. (3 points each. No partial credit.) The questions on this page are multiple choice. They do not require an explanation. For each question, circle your choice for the correct answer(s). There may be more than one correct choice. Circle ALL answers that must be true about the given statement. (a) The function h ( x ) = x 5 - x 3 + 2 x 2 x 3 - 3 x 2 (i) is undefined for x = 0 and x = 3 . (ii) has a horizontal asymptote of y = - 2 / 3 . (iii) has vertical asymptotes at x = 0 and x = 3 . (iv) approaches -∞ as x approaches . (v) has a horizontal asymptote of y = 1 . (b) If a function f is continuous at x = a , then (i) lim x a f ( x ) exists. (ii) lim x a f ( x ) = f ( a ) . (iii) lim x a f ( x ) = f ( a ) . (iv) f is differentiable at x = a . (v) none of (i)-(iv) must be true. (c) If lim x 3 g ( x ) = 5 for some function g , then (i) g (3) = 5 . (ii) g is continuous at x = 3 . (iii) lim x 3 - g ( x ) = lim x 3 + g ( x ) . (iv) g (3) = 5 . (v) g is differentiable at x = 3 .
3 2. Suppose A ( t ) is a function that gives the average high temperature (in o F ) in Ann Arbor as a function of t measured in months where t = 0 represents January (the coldest month in Ann Arbor). (a) (2 points) Puerto Montt, a city in Chile, is approximately the same distance from the equator as Ann Arbor, but it is in the southern hemisphere where the warmest month is January.

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