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Exam1_Solutions_F09

# Exam1_Solutions_F09 - Math 115 First Midterm Name...

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Math 115 / Exam 1 (October 13, 2009) page 2 1 . [12 points] For each problem below, circle all of the statements that MUST be true. (The three parts (a)–(c) are independent of each other. No explanations are necessary.) a . [5 points] Suppose f is an increasing diﬀerentiable function with domain ( -∞ , ) so that f (1) = 1 and f ( - 1) = - 1. f is linear. There is a number c so that f ( c ) = 0. lim x 1 f ( x ) = 1 lim x →∞ f ( x ) = f 0 (1) 0 b . [3 points] Suppose g ( t ) is the mass (in grams) of mold on a wedge of cheese in a refrigerator t days after it was abandoned. This mass grows exponentially as a function of time for two weeks, when it is ﬁnally thrown away. The graph of g is concave up. The continuous growth rate of g is less than the daily growth rate. The amount of time it takes for the mass of mold on the cheese to triple is 1.5 times the amount of time it takes for it to double. c . [4 points] If f ( x ) = g ( x ) h ( x ) and h (3) = 0 then The graph of f has a vertical asymptote at x = 3. 3 is not in the domain of f . f is not continuous on [ - 2 , 2]. lim x 3 f ( x ) does not exist.
Math 115 / Exam 1 (October 13, 2009) page 3 2 . [12 points] Suppose that the line tangent to the graph of f ( x ) at x = 3 passes through the points (1 , 2) and (5 , - 4).

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Exam1_Solutions_F09 - Math 115 First Midterm Name...

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