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! ! 3. Find lim x "2 e t 2 x #1 $ dt 2 x 3 # 4x A. 0 B. ! e 4 12 ! C. e 3 8 © 2011 www.mastermathmentor.com - 8 - Demystifying the BC Calculus MC Exam ! D. "e 6 E. nonexistent _______________________________________________________________________________________ 4. A particle moves in the xy-plane so that the position of the particle at any time t is given by x( t) = cost and y( t) = sin 2 dy 4t. Find lim t "0 dx . A. -32 B. -16 C. -8 D. -4 E. 0 ! _______________________________________________________________________________________ 5. A population of bacteria is growing and at any time t, the population is given by 500 1+ 2 t " % $ ' . Find the # t & maximum limit of the population. A. 500 B. 500 + e C. 500e D. 2 + ln500 E. ! ! ! ! ! 500e 2
! ! B1. Integration by Parts What you are finding: When you attempt to integrate an expression, you try all the rules you have been given to that point - typically power, substitution, and the like. But if these don’t work, integration by parts may do the trick. Integration by parts is usually used when you are need to find the integral of a product. How to find it: Integration by parts states that # u dv = uv " # v du + C. To perform integration by parts, u = v = set up: . You need to fill in the u and the dv from the original problem. Determine du = dv = du and v, then substitute into the formula. You are replacing one integration problem with another that might more easily be done with simple ! methods. The trick is to determine the u and the dv. Functions that can be “powered down” are typically the u and functions that have repetitive derivatives (exponential and ! trig) are typically the dv. ! ! ! 6. " 2x cos4x dx = A. x sin4x + cos4x + C B. 2 ! © 2011 www.mastermathmentor.com - 9 - Demystifying the BC Calculus MC Exam x 2 1 sin4x + cos4x + C 8 C. 8x sin4x + 32cos4x + C D. 8x sin4x " 32cos4x + C E. x sin4x " cos4x + C 2 ! _______________________________________________________________________________________ ! ! 7. " x 2 e 2x dx = A. e 2x 2x 2 ( " 8x +16) + C B. e ! 2x 2x 2 ( " 8x + 2) + C C. e 2x x 2 # x 1& % " " ( + C $ 2 2 2' D. e 2x x 2 # x 1 & % " + ( + C $ 2 2 4 ' E. ! ! " % $ ' + C # 3 & e 2x x 3
Page 1: ! A. Limits - L’Hopital’s Rule
Page 5 and 6: ! ! ! B2. Integration using Partial
Page 7 and 8: ! C. Improper Integrals What you ar
Page 9 and 10: ! D. Euler’s Method What you are
Page 11 and 12: ! E. Logistic Curves What you are f
Page 13 and 14: 29. (Calc) The yellow bird in the p
Page 15 and 16: ! 34. A curve C is defined by the p
Page 17: 40. An object moving in the xy-plan

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