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fall2008

# fall2008 - MATH 1241 FINAL EXAM PART I(Calculators not...

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MATH 1241 FINAL EXAM FALL, 2008 PART I (Calculators not allowed) 1. If g ( x ) = x 2 + e x , then g 0 ( x ) = (a) x 2 + e x (b) 2 x + e x (c) x 2 + xe x - 1 (d) 2 x + xe x - 1 (e) 2 + e x 2. d dx ( x sin x ) = (a) sin x (b) cos x (c) - cos x (d) sin x - x cos x (e) sin x + x cos x 3. If f ( t ) = ln t t , then f 0 (2) = (a) ln 2 2 (b) 1 - ln 2 4 (c) 1 + ln 2 4 (d) 1 2 (e) 1 4 1

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4. If f ( x ) = (3 x 2 + 1) 4 , then f 0 ( x ) = (a) (3 x 2 + 1) 4 (b) 24 x (3 x 2 + 1) 3 (c) 4(3 x 2 + 1) 3 (d) 4(6 x ) 3 (e) 4(6 x + 1) 3 5. Which of the following is correct? (a) d dx (ln(3 x 2 + 4)) = ln(3 x 2 + 4) (b) d dx (ln(3 x 2 + 4)) = 1 3 x 2 + 4 (c) d dx (ln(3 x 2 + 4)) = 1 6 x (d) d dx (ln(3 x 2 + 4)) = ln 6 x (e) d dx (ln(3 x 2 + 4)) = 6 x 3 x 2 + 4 6. Let h ( s ) = sin 2 (2 s ). Then h 0 ( s ) = (a) 4 sin(2 s ) cos(2 s ) (b) 2 sin(2 s ) cos(2 s ) (c) cos 2 (2 s ) (d) 2 cos 2 (2 s ) (e) 2 cos( s ) + 2 2
7. Let f ( x ) = x 3 - 3 x 2 + 7. Which of the following statements is true? (a) f is increasing on ( -∞ , ) (b) f is decreasing on ( -∞ , ) (c) f is increasing on (0 , ) (d) f is decreasing on (0 , 2) (e) f is increasing on (0 , 2) 8. Consider the graph of the function f : Which of the following is correct? (a) lim x 1 f ( x ) = 4 (b) lim x 1 f ( x ) = 3 (c) lim x 1 f ( x ) = 2 (d) lim x 1 f ( x ) = 1 (e) lim x 1 f ( x ) does not exist 9. lim x →∞ x 2 + 1 xe x + 1 = (a) (b) 1 (c) - 1 (d) 0 . 01 (e) 0 3

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10. Let g ( x ) = 3 x 2 + 1. Which of the following is the equation of the tangent line to the graph of g at x = 1? (a) y - 6 = 4( x - 1) (b) y = 4( x - 1) (c) y = 6( x - 1) (d) y - 4 = 6( x - 1) (e) y - 6 = 6( x - 1) 11. lim x 0 2 x 2 - x 10 x + 1 = (a) - 1 / 10 (b) 0 (c) (d) 1 / 5 (e) -∞ 12. Let f ( x ) = 1 x 2 + x + 3 . Then f has a local maximum at x = (a) 0 (b) 1 / 2 (c) 1 (d) - 1 / 2 (e) - 1 4
13. Let f ( x ) = 6

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fall2008 - MATH 1241 FINAL EXAM PART I(Calculators not...

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