MATH 132 FINAL EXAM FALL 2009 This exam should have 20 questions 5 points each If you do not have a PENCIL to mark your card please ask to borrow one from your proctor Write your ID NUMBER not your SS number on the six blank lines on the top of your answer card using one blank for each digit Shade in the corresponding boxes below Also Print your name at the top of your card You may bring along a 5 x 7 card and the calculator you used for the first three exams The needed data for power series is contained on the last page of this booklet 1 Evaluate 0 38 B cos B dB 1 E F G H I J 1 K L 1 M 2 Evaluate E F G 1 H 1 I 1 J 1 K 1 L M 1 N 1 1 B sin 2x B 132f09 4 2 2 3 Use partial fractions to evaluate 1 B B B 1 B E 1 24 F 1 38 G 1 46 D 1 56 E 1 69 F 1 75 G 1 80 H 1 91 I 2 14 Find what becomes of the integral 4 x B B when you make the substitution x 2 tan 1 1 E 8 F sec G ec 2 H cot I sc J K t 8 L 8 M cot N csc 132f09 4 3 5 Find the area of the region enclosed by 0 B B 8 0 B B E 1 F G 1 H I J 16 K L M N 6 Find the volume of the solid you get by revolving the region enclosed by the curve B C the lines B and C about the B axis A 1 F 1 G 1 H 1 I 2 1 J 1 K 4 1 L 1 M 1 N 1 132f09 4 4 7 Suppose S is the solid whose base in the region bounded by the parabola C 4 B and the line y 0 and whose cross sections perpendicular to the y axis are squares For each y between 0 and 4 find a formula for the cross section A y A y B y G C H y I C J y K C L y M C N C Calculate the arc length of the curve y A F G H I J K L M N x x 132f09 4 5 9 Determine whether the improper integral and if so determine its value 8 0 1 B B converges A 0 B 2 C H 4 I J K L 8 M N 3 1 A force of 20 N is required to hold a spring stretched 5 m beyond its natural length How much work is done in stretching it from 5 m to 10 m beyond its natural length A 50 J B 90 J C 110 J D 130 J E 150 J F 170 J G 90 J H 210 J I 230 J J 250 J 132f09 4 6 C 11 Find the solution to the initial value differential equation C C E C F C G C H C I C J C K C L C 68 M C 38 N C 9 12 Find the sum of the E F G H I J K L M N 1eometric series 132f09 4 7 13 If cos 2x a8 B8 3 Q 6 38 3 E F G H I J K L M N 14 Find the function whose Maclaurin series is B B B B E 38 B B 9 B G 68 B H B I B J B K B L B M 8 B N 8 B find 8 B a 132f09 4 8 a8 x 1 8 6 15 If 8 at c A 0 B G H I J 1 is the Taylor series of the function f x cos x then find the value of a the coeficient of the term a x 16 K L M N 16 Find the interval of convergence of the power series 8 E B F B G B H B E 4 B 4 F 4 B 4 G 0 B 4 H 0 B 4 I 0 B 4 J B B 8 8 132f09 4 9 17 Find the 4 2 term in the binomial series for the function f x 1 B E B F B G B H B I B J B K B L B M B N B Using the error formula for alternating series what error do you make by approximating S 8 E B C D E F G H I J 8 8 8 8 by S i e the sum of the first three terms 132f09 4 10 Find the term a in the Maclaurin series of f B B 38 B B A 0 B 1 C 1 D E F K L I N Find the function whose Maclaurin series is 8 E 38 B F 9 B G B H 38 B I 9 B J B B K L 8 B M B N 68 B 8 B 8 8 8 132f09 4 11 Frequently used Maclaurin Series B B B B8 lBl 8 B x B B 38 B B 9 B B x B x arctan x B B3 3 B a aB 68 B B B B x B x 8 8 B 8 8 x B x 8 B 8 8 x B B x B x B5 5 a a x 8 8 B B a a a B x 8 lBl lBl lBl 8 B28 1 28 1 8 B8 8x B a Bn lBl n n 8 B8 8 lBl
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