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math_112_test_1_winter_2011

# math_112_test_1_winter_2011 - Math 112 Winter 2011 Exam 1...

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Unformatted text preview: Math 112 Winter 2011 Exam 1 SOLUTIONS Multiple Choice.. 1. The expression 5 ln( x + 1)- 2 ln(4) + 2 ln( x + 7)- 1 2 ln( x ) can be combined into a single logarithm, i.e. ln[ f ( x )]. Find f ( x ). a) f ( x ) = 1 5 x +1 · 2 2 x +3 b) f ( x ) = ( x + 1) 5 16( x + 7) 2 √ x c) f ( x ) = 7 x + 19 4 x d) f ( x ) = 5 x +1 · 2 2 x +3 e) Ans f ( x ) = ( x + 1) 5 ( x + 7) 2 16 √ x f) None of the above. 2. Find all vertical asymptotes of x 2- 4 x 2- 2 x . a) x = 2 b) Ans x = 0 c) x = 0 , 2 d) x =- 2 , 2 e) x =- 2 , f) x =- 2 , , 2 g) There are none. h) There are infinitely many. i) None of the above. 3. Which of the following functions is odd? a) Ans x 3 + x b) x 3 + 6 x 2 + 9 x c) x x- 1 d) cos( x ) e) More than one is odd. f) None of the above. 4. Find all horizontal asymptotes of f ( x ) = 2 x 2 + 11 x + 12 2 x 2 + x- 3 . a) y = 3 / 2 , 1 b) y = 3 / 2 c) Ans y = 1 d) y = 3 / 2 , 1 ,- 4 e) y = 2 f) y =- 4 g) None of the above. 5. A particle is moving in a straight line so that its distance traveled after t seconds is given by s ( t ) = e t + 1 meters. Find the average velocity of the particle over the time interval [0 , ln(2)]. a) Ans 2 / ln(2) m/s b) 3 m/s c) 3 / ln(2) m/s d) 0 m/s e) ln(2) m/s f) 2 m/s g) e 2- 1 m/s h) 1 / ln(2) m/s i) None of the above. 6. Find c such that f ( x ) = braceleftbigg x 3 + cx + 3 if x ≤ 2 4 x + c if x > 2 is continuous everywhere. a) Ans -3 b)-1 c) d) 1 e) 3 f) 2 g) No such c exists. h) None of the above. 7. The graph of f is shown below. What is the equation of the tangent line to the graph at the point (2 , 3)?...
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math_112_test_1_winter_2011 - Math 112 Winter 2011 Exam 1...

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