140Bquiz1csols

140Bquiz1csols - 1 MATH 140B QUIZ#1 Solutions Date: Fall...

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Unformatted text preview: 1 MATH 140B QUIZ#1 Solutions Date: Fall 2007 1. i) True. A line with positive slope ( > 0) goes upward to the right. ii) True. If f ( x ) = x- 3 then f (3 / ) = (3 / )- 3 = 3- 3 = 0 . iii) False. By definition, they are not directly proportional due to the constant term- 3 . Therefore the correct answer is C). 2. Odd degree and negative leading coefficient means: i) False. It goes down to the right. For instance take a line with negative slope. ii) True. It goes up to the left. iii) True. It goes up to the left, down to the right, and is continuous, so it will cross the x-axis at least once. Therefore the correct answer is E). 3. Since R = 1 / 2 cm and v = 1 when r = 1 / 4 , we have 1 = k ( 1 4- 1 16 ) = k ( 4 16- 1 16 ) = k ( 3 16 ) , so k = 16 / 3 and v ( r ) = 16 3 ( 1 4- r 2 ) . Evaluating this function, and getting a common denominator to subtract fractions, v parenleftbigg 1 3 parenrightbigg = 16 3 parenleftbigg 1 4- 1 9 parenrightbigg = 16 3 parenleftbigg 9- 4 36 parenrightbigg...
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