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test2practice - MATH 151 SPRING 2006 COMMON EXAM II VERSION...

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MATH 151, SPRING 2006 COMMON EXAM II - VERSION A LAST NAME, First name (print): INSTRUCTOR: SECTION NUMBER: UIN: SEAT NUMBER: DIRECTIONS: 1. The use of a calculator, laptop or computer is prohibited. 2. In Part 1 (Problems 1-13), mark the correct choice on your ScanTron form No. 815-E using a No. 2 pencil. For your own records, also record your choices on your exam! ScanTrons will be collected from all examinees after 90 minutes and will not be returned. 3. In Part 2 (Problems 14-17), present your solutions in the space provided. Show all your work neatly and concisely and clearly indicate your final answer . You will be graded not merely on the final answer, but also on the quality and correctness of the work leading up to it. 4. Be sure to write your name, section number and version letter of the exam on the ScanTron form . THE AGGIE CODE OF HONOR “An Aggie does not lie, cheat or steal, or tolerate those who do.” Signature: DO NOT WRITE BELOW! Question Points Awarded Points 1-12 48 13 9 14 14 15 9 16 10 17 10 100 1
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PART I 1. (4 pts) If g ( x ) = ( x 3 + x ) 5 , then g 0 ( - 1) = (a) 320 (b) 160 (c) 80 (d) 40 (e) 0 2. (4 pts) 4 ln 2 + ln 3 4 = (a) ln 12 (b) ln 6 (c) ln 25 (d) ln 54 (e) ln 24 Exam continues on next page 2
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3. (4 pts) Find the slope of the tangent line to the curve sin( xy ) = x 2 - 3 at the point 3 , π 3 . (a) - 2 (b) - 2 - 3 π (c) - 2 + 3 2 π (d) - 2 - π 3 (e) - 2 + π 3 4. (4 pts) If f ( x ) = 1 x + 2 , then the inverse function of f ( x ) is Exam continues on next page 3
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5. (4 pts) lim t 0 sin 2 (4 t ) 2 t 2 = 6. (4 pts) If f ( x ) = x + sin( x ) + 2 e 3 x and g ( x ) = f - 1 ( x ) , then g 0 (2) = Exam continues on next page 4
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7. (4 pts) If h ( x ) = sin 2 (3 x ) , then h 00 ( x ) = (a) 6 cos(3 x ) (b) 18(cos 2 (3 x ) - sin 2 (3 x )) (c) 18 (d) 9(cos 2 (3 x ) - 1) (e) 9 sin 2 (3 x ) 8. (4 pts) Find the linear approximation of f ( x ) = 1 x at a = 4 . Exam continues on next page 5
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9. (4 pts) The length of leg AB of right triangle ABC increases at a rate of 2 inches per second and the length of leg BC increases at a rate of 6 inches per second. At what rate in inches per second does the hypotenuse increase when AB = 3 and BC = 4 ? 10. (4 pts) lim x →-∞ 2 - e 5 x 1 + e 2 x = Exam continues on next page 6
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11. (4 pts) A curve C is given by the parametric equations x = 2 t 3 - 3 t 2 , y = t 2 - t . Find all horizontal and vertical tangents. (a) horizontal tangent at t = 0 and t = 1 , vertical tangent at t = 1 2 . (b) horizontal tangent at t = 1 2 , vertical tangent at t = 0 and t = 1 . (c) horizontal tangent at t = - 1 and t = 1 , vertical tangent at t = 2 . (d) horizontal tangent at t = 2 , vertical tangent at t = - 1 and t = 1 . (e) None of the above
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