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# 00quiz2 - on the axes below Make sure to label values of...

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SECTION: NAME: APSC171 Quiz II.a(White) 25 MINUTES November 16, 2000 1. You are given a continuous function, y = f ( x ) which has first and second derivatives which are continuous. You may assume the following information about this function: (a) f is positive on ( - 1 , 1) and negative on ( -∞ , - 1) (1 , ); (b) f 0 is positive on ( -∞ , 0) and negative on (0 , ); (c) f 00 is positive on ( -∞ , - 1 3 ) ( 1 3 , ) and negative on ( - 1 3 , 1 3 ); (d) There is only one asymptote, namely y = - 1; (e) f (0) = 2. Sketch the graph of

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Unformatted text preview: on the axes below. Make sure to label values of all signiﬁcant points on this graph. [3] 2. Find the most general antiderivative of f ( x ) = e 3 x + sin(2 x ) 2-x √ x 3 [3] TURN OVER FOR #3 3. Find the area of the smallest right-angled triangle that can be drawn in the ﬁrst quadrant so that the sides adjacent to the right angles lie on the x-axis and the y-axis, and the hypotenuse passes through the point (2,7). [4]...
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