# ASU MAT 266 - mat266_ex3_0 (6 pages)

Previewing pages*1, 2*of 6 page document

**View the full content.**## mat266_ex3_0

Previewing pages
*1, 2*
of
actual document.

**View the full content.**View Full Document

## mat266_ex3_0

0 0 38 views

- Pages:
- 6
- School:
- Arizona State University
- Course:
- Mat 266 - Calculus for Engineers II

**Unformatted text preview:**

MAT 266 Test3 MAT 266 TEST 3 ANSWERS SOLUTIONS SoMSS ASU Directions 1 There are 14 questions worth a total of 60 points 2 Questions 1 10 are Multiple Choice worth 4 points each to be answered on the supplied SCANTRONS 3 Questions 11 14 are Free Responses worth 5 points each and are to be answered in the space provided on the test 4 Read all the questions carefully 5 For the Free Response you must show all work in order to receive credit 6 When possible box your answer which must be complete organized and exact unless otherwise directed 7 Always indicate how a calculator was used i e sketch graph etc 8 No calculators with QWERTY keyboards or ones like TI 89 or TI 92 that do symbolic algebra may be used Honor Statement By signing below you confirm that you have neither given nor received any unauthorized assistance on this exam This includes any use of a graphing calculator beyond those uses specifically authorized by the Mathematics Department and your instructor Furthermore you agree not to discuss this exam with anyone until the exam testing period is over In addition your calculator s program memory and menus may be checked at any time and cleared by any testing center proctor or Mathematics Department instructor Signature Date 1 MAT 266 Test3 1 n x n n 4 1 Find the interval of convergence of the series n 1 Select the correct answer a 0 2 b 1 2 c 1 1 d diverges everywhere e None of these 2 Suppose that the radius of convergence of the power series cn x n is 16 What is the radi n 0 us of convergence of the power series cn x 2 n n 0 Select the correct answer a 256 b 4 c 1 d 16 e None of these 3 Find the radius of convergence of the series n 1 8n x n n 5 2 Select the correct answer a R 8 b R 1 8 c R 1 d R 5 e None of these 4 Find the Taylor polynomial T3 for the function f x ln x at the number a 1 Select the correct answer a c e 1 1 x 1 x 1 2 x 1 3 3 2 1 1 x 1 x 1 2 x 1 3 4 2 b d 1 1 x 1 x 1 2 x 1 3 2 3 1 1 x 1 x 1 2 x 1 3 4 2 None of the above 5 Find the sum of the series 2 n 0 1 n n Select the correct answer a 1 e b e c e 2 d e 2 e None of these 2 MAT 266 Test3 6 Evaluate the indefinite integral tan 1 t 2 dt as a power series 2 n 1 x3 x5 x 7 n x The MacLaurin series for tan x x 1 3 5 7 2n 1 n 0 Select the correct answer 1 a C n 0 c C n 0 e 1 n t 4 n 3 2n 1 4n 3 b C n 0 1 n t 4 n 2 2n 1 4n 3 d C n 0 1 n t 4n 3 4n 3 1 n t 2 n 2 2n 1 None of the above 2 7 Find the first three nonzero terms in the MacLaurin series for the function f x e x cos 4 x Select the correct answer a 1 17 x 2 19 17 x 4 c 1 9 x 2 19 17 x 4 e None of the above b 1 9 x 2 11 17 x 4 d 1 9 x 19 17 x 2 8 Eliminate the parameter to find the Cartesian equation of the curve x cos y sec 0 2 Select the correct answer a y x 2 b y x c y 2 x d y 1 x e None of these 9 Find the radius of convergence of the binomial series expansion of the f x 1 2 x 2 Select the correct answer a R 1 b R 1 2 c R 2 d R 4 e None of these 10 Find parametric equations to represent the line segment from 1 2 to 10 6 Select the correct answer a x 10 8t y 1 11t 0 t 1 c e x 1 11t y 6 8t 0 t 1 b x 1 11t y 2 8t 0 t 1 d x 1 11t y 8t 0 t 1 None of the above 3 MAT 266 Test3 11 Find the polar equation for the curve represented by the given Cartesian equation x y 4 Select the correct answer 2 cos sin c r 4 cos sin a r e r 4 cos sin r 2 cos sin b r d 4 cos sin 12 Set up the integral for the length of the curve x 3t 2 y 2t 3 0 t 1 Select the correct answer 1 1 1 b 6t 2 6t 2 2 dt c 6t 6t 2 dt a 6t 2 6t 2 2 dt 0 0 0 1 1 e 36t 2 36t 2 2 dt f none of these d 6t 6t 2 2 dt 0 0 FREE RESPONSE sin x x x 0 x3 13 Use series to evaluate lim 4 MAT 266 Test3 14 Use the power series representation of f x sin x to find a power series representation for g x x sin x 2 m5 m m 1 3 15 Test the series for convergence or divergence 5 MAT 266 Test3 16 Use the Binomial Theorem to find the first 3 terms of the MacLaurin Series for f x 3 5 x and use it to estimate 3 5 08 1 2 17 5 pts Find the area bounded by the curve x t y t and the line y 4 5 t t 18 5 pts Find the slope of the tangent line to the polar curve r 2 when 19 5 pts Find the area of the region that lies inside the curve r 3cos and outside the curve r 1 cos 20 5 pts Find the exact coordinates of the highest point on the curve x 15tet y 3te t 6

View Full Document