271_FinalRev_SU11 - MAT 271 Summer 2011 Calculus II Scott...

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MAT 271, Summer 2011 Calculus II, Scott Zinzer Final Exam Review Final Exam Review. Sections 5.5, 6.1-6.6, 7.1-7.7, 8.1-8.6, 9.1-9.4, 10.1-10.4 You are expected to know complete solutions to all examples, homework problems, and recitation problems. Any of those such items may (and some will) appear on the exam. The first part of the final exam review consists of the review problems for the first three exams. The problems appearing below cover only material from sections 9.3, 9.4 and 10.1-10.4. The following problems are meant to help focus your study for the exam; they should not be considered a complete list of all concepts or types of problems appearing on the exam. Free Response (1) Write out the first three terms of the Taylor series for f ( x ) = 1 /x centered at a = 1 then write the series using summation notation. (2) Write out the first three terms of the Taylor series for f ( x ) = e 3 x centered at a = 0 then write the series using summation notation. (3) Write the remainder term R n ( x ) for the Taylor series for
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Unformatted text preview: f ( x ) = sin x centered at a = 0. (4) Use Taylor series to evaluate lim x → x 2 / 2-1 + cos x x 4 . (5) Consider the parametric curve x = t 2 + 4, y = 6-t for-∞ < t < ∞ . Eliminate the parameter to obtain an equation in x and y . Evaluate dy/dx at (5 , 5). (6) Find an equation of the line tangent to the cycloid x = t-sin t , y = 1-cos t at the point corresponding to t = π/ 6. (7) Write the equation r 2 + r (2 sin θ-6 cos θ ) = 0 in Cartesian coordinates and identify the corresponding curve. (8) Find all the points where the curve r = 4+2 sin θ has vertical and horizontal tangent lines. (9) Find the area enclosed by all the leaves of the rose r = 3 sin 4 θ . (10) Find the area inside the lima¸con r = 2 + cos θ and outside the circle r = 2. (11) Graph the conic section x 2-y 2 / 2 = 1. (12) Graph the conic section x 2 / 4 + y 2 / 25 = 1. (13) Graph the conic section r = 3 1-2 cos θ ....
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  • Fall '08
  • SURGENT
  • Calculus, Parametric equation, Conic section

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