Spring07-Test2

Spring07-Test2 - 8 !!!!!!!!!!! 2-at = 1 (i.e., a = 1) to...

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Math 1205 -- Test 2 28 Mar 2007 NAME: You will be graded on how well and fully you support your work! Use only methods developed in class. CRN: 1 .[8] Evaluate lim x Æ 0 tan H 3 L ÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅ . 2 .[10] For what values of a and b will f H L = 9 ax < 2 2 - bx + 4 ¥ 2 be differentiable for all ? 3 .[21] Differentiate the following functions: (a) H L = xe 2 ÅÅÅÅÅÅÅÅÅÅÅÅ + 1 (b) g H t L = è!!!!!!!!!!!!!!!! !!!!!!!!! log H sec H L L 3 (c) y = 2
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4. [9] Give all values of x for which f H L = 2 cos H L + has a horizontal tangent line. 5. [10] Find the second derivative of H L = tan - 1 H 2 L . 6 .[12] Suppose y is a differentiable function of that satisfies 2 - xy + 2 = 3. (a) Use implicit differentiation to find dy ÅÅÅÅÅÅÅ dx . (b) The normal line to the curve at (-1,1) intersects the curve at what other point? 7 .[10] If and g are the graphs shown, and h H L = H H LL , determine ' H 2 L , if it exists. 1 2 3 4 5 6 7 1 2 3 4 5 6 7 f g ' H 2 L = ___ ___ ___ _
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8 .[10] Use the tangent line approximation of f H x L = -
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Unformatted text preview: 8 !!!!!!!!!!! 2-at = 1 (i.e., a = 1) to approximate I 3 2 M . 9 .[10] The position function, s H t L , for a particle moving on a coordinate line on the interval @ 0, 6 D is given by: s H t L t 2 t 1 2 t-1 1 < t 2-t 2 + 6 t-5 2 < t 4 t 2 2-6 t + 19 4 < t 5 13 2-t 5 < t 6 a) Plot v H L . 1 2 3 4 5 6 t-2-1 1 2 v H t L Using interval notation, H , b L , answer each of the following questions. b) When is the particle moving to the right? c) When is the particle moving to the left? d) When is the particle slowing down? e) When is the particle at rest?...
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This test prep was uploaded on 04/01/2008 for the course MATH 1205 taught by Professor Fbhinkelmann during the Fall '08 term at Virginia Tech.

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Spring07-Test2 - 8 !!!!!!!!!!! 2-at = 1 (i.e., a = 1) to...

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