MATH 132 FINAL EXAM F12M132 4 1 This exam should have 20 multiple choice questions 5 points each If you don t have a PENCIL to mark your card please ask to borrow one from your proctor Write your ID NUMBER not your SS number in the six boxes on the side of your answer card and then shade in the corresponding numbers The needed data for trigonometric functions and power series is contained on the last page 1 4 1 Use substitution to evaluate 0 tan B B B E F G H I J K L I N e 2 Use integration by parts to evaluate 1 B 68 B B E F G H I J K L M N 132F12 4 2 3 Using partial fractions find a solution to B2 B B B A 8 2B 1 B B2 B C 68 B2 B D 68 B 68 B E 68 BB 68 B F 68 B G 68 x B 1 B L 68 B B B M 68 BB N 68 BB 4 Find what becomes of the integral B 38 1 A 38 B 9 C 38 D 9 E F G 38 H 9 I 38 J 9 1 B B B when you make the substitution 132F12 4 3 5 Find the area of the region enclosed by the curve C C 2 2 B B and the line E F G H I J K L M N 6 Find the volume of the solid obtained by rotating the region enclosed by the curve B C the lines C C and the C axis about the y axis E 1 F 1 G 1 H 1 I 1 J 91 K 1 L 1 M 1 N 1 132f12 4 4 7 Find the arc length of the curve B C 2 C E 4 F 8 G 14 3 H I 2 J K L M 20 J 8 Find the value of the improper integral 0 E 0 B 2 C 4 D 6 I 8 J K L M N 3 1 B B B if it converges 132f12 4 5 9 Find the solution to the initial value differential equation E C F C G C H C I C 68 J C 68 K C L C M C N C 1 Find the sum of the infinite series E 3 F 4 G H I J 2 K L M 4 N 8 8 8 C C C f 1 Approximate the sum 8 8 8x with an error of less than 2 x 10 3 E 367 F 371 G 384 H 396 I 408 J 414 K 429 L 437 M 4458 N 452 12 Find the complete interval of convergence either absolute or conditional of the power series 8 A B F B G B H B I B J B K B L B M B N 8 B 8 8 8 132f12 4 7 13 Find the Taylor polynomial of order for 0 B B at B E B B F B B G B B H B B I B B J B B K B B L B B M B B N B B 14 If the Maclaurin series for B B is 8 B8 then find E F G H I J K L M N 8 c 132f12 4 8 Using the Maclaurin series for 68 1 B with an error 0 002 approximate 68 B B E 0 109375 F 0 210432 G 0 342871 H 0 465732 I 0 543876 J 0 623149 K 0 743987 L 0 841762 M 0 954129 N 1 097658 16 Find the Maclaurin series for the function B 8 B 8 2 8 2 E 8 0 F 8 0 G 8 0 I 8 0 J 8 8 B 8 8 8 L 8 8 N 8 8 B 8 8 K M 8 B 8 2 8 1 8 B 8 4 8 3 H 8 0 8 B 8 4 8 2 8 B 8 8 8 B 8 8 8 B 8 8 8 B 8 8 B 8 B 132f12 4 9 Find the Taylor series for 0 B B B centered at E B B F B B G B B H B B I B B J B B K B B L B B M B B N B B 8 If 38 B 8 B 8 centered at A F G H I J K L M N 1 8 is the Taylor series for the function 38 B 1 then find the coeficient c of B 1 2 132f12 4 10 19 From the formula of the Binomial Series we get that B 8 B8 with 8 A 0 B G H I J K L M N 20 Using the Alternating Series Estimation Theorem and the Maclauren Series for eB estimate B B with an error less than or equal to 1 x 10 E 0 B 2765 C 3876 D 0 5762 E 0 F 0 K 0 L 0 M 523 N
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