M134-Test1-F09 - x cos(3 x ) sin(5 x ) cos(2 x ) sin(6 x )...

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MCS @UTM MAT 134Y5Y Term Test 1 Friday, Oct 9, 2009 Last Name: Given Name: Student #: Tues 11 12 1 5 6 7 Thurs 11 12 1 5 6 7 Please Circle Your Tutorial. Allowed Aids: Non-graphing Calculator Duration: 110 minutes. Answer all questions. Show your work. There are 6 pages including this cover page but not including the signature page. Qn# Value Score 1 10 2 10 3 10 4 10 5 10 Total 50 1
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1. (a) Solve | 3 x - 1 | < 1 . Show your answer in interval notation. [4] (b) Find f - 1 when y = f ( x ) = ln( e x + 1) . [4] (c) Let f ( x ) = x 2 - 4 , g ( x ) = x + 4 . Find formulas for f g and g f . [2] 2
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2. (a) Sketch the graph of y = sin(2 πx - π ) , 0 x 1 . [4] (b) Sketch the graph of y = sin - 1 ( x ) . [2] (c) Find the value of sin - 1 ( tan ( 15 π 4 )) . [2] (d) What are the values of x ± - π 2 , π 2 ² that belong to the domain of y = sin - 1 (tan x ) ? [2] 3
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3. Evaluate the following limits. (a) lim x →- 3 x 2 + x - 6 x 2 + 4 x + 3 [4] (b) lim
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Unformatted text preview: x cos(3 x ) sin(5 x ) cos(2 x ) sin(6 x ) [3] (c) lim x + 6 x + 1 x 2-1 + x [3] 4 4. Let f ( x ) = 3 x 2 + 1 x-1 . (a) Find all horizontal, vertical, and oblique asymptotes of f . [6] (b) Guess the graph of f and draw a rough sketch. [2] (c) Does f have an inverse? State ( briey ) a reason for your answer. [2] 5 5. Let f ( x ) = 4 e 1 /x + 6 6 e 1 /x + 9 . (a) Find lim x -e 1 /x . [2] (b) Find lim x + e 1 /x . [2] (c) Which of the following statements is true? Justify your answer. [6] (i) f has a vertical asymptote at x = 0 . (ii) f has a jump discontinuity at x = 0 . (iii) f has a continuous extension to x = 0 . 6...
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M134-Test1-F09 - x cos(3 x ) sin(5 x ) cos(2 x ) sin(6 x )...

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