Rational Function - Calculus - Solved Quiz, Exercises of Calculus

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Math 106 A and B <— circle your section Quiz 04 page 1 02/10/12 Name Supgisted Salhi 1. Suppose you have to find an integral of the form / “3 dx, where p and q are polynomials. Suppose p(x) = (x — 4)4(a + 2)(x — 1/2)?. 1A. What is the partial fraction decomposition of az) here? A, 8 ,¢ 2. + £.. 4 £ x1 (xu) (4)? x4) ¢ 1B. What is the biggest degree g(x) can have such that polynomial long-division is not required as a necessary first step in finding / a) ae) ae? po diston 6 reed dum ds (6) < (2) ho«, cltg(P) = Yt/+2=>2 © He Answer 6 4 2. Suppose the partial fraction decomposition of some rational function r(x) is Gor What is [r@az af{ > 4 [iba | t x -5)6 ob On Sma a af _ = arte - -5 4“ (:dum > x-5) 3. For integration by parts, the mnemonic device “LIATE” is suggested. What do its letters stand for and how is it used? L- bg . Whon dai an ialegrohiom by pe a - Wem ) ian poder ) Cun uw the = Ode . ‘ tee fico he opr he. agp 5 . hawt in fas ik, E - erpontntiak y 4, Find | x cos x dz using integration by parts. Show all your steps. oy ane pike) ‘ Au =i, v’=s* 9 and Ve [lx aca GOX L Jx wax 2 uv- [ve' & X 50 X — |(oix 1) a X Sx — (-@x) +c u