Calculus 1301A/B Study Guide - Midterm Guide: Alternating Series Test, Alternating Series, Direct Comparison Test

/ Math123FallTEast - MX Jalan - X e A Secure | https://bbcsulb.desirežlearn.com/dz//le/content/4041/4/viewcontent/4441994/View * @ : # Apps Pearson Sign In B Free Office 365(use fie D offices Hurs Fall-201 Y Question involving ar % Assignment (o -- Mat Q Fevica Cuestiors: CE Q Program Design &D CSI-117 midterm Flus Pctween the Panels: Math 123 - Exam 3 (Sample 1) 1. Determine whether the sequence converges or diverges. If it converges, find the limit. _ 3n - n (b) {1, -34-, ...} (e) {V3, V3/3, 3/3/3, ...} (a) on -2n + n 2. Determine whether the series converges or diverges. If it converges, find the sum. ( #1 () È 3. (a) Find the sum of the first 100 terms for the sequence I , and then find the sum s. Ln2 + 4n +3 n=1' (b) Express 0,1234 = 0.123423234... as a ratio of integers. 4. (a) The function f(x) = -1.1 Inx satisfies the hypothesis of the integral test (i.e., it is continuous, positive, and decreasing on [2, x)). Apply the integral test to determine if E converges or diverges. Sni. (b) Apply an appropriate test to determine whether converges or diverges. 5. Determine whether the series converges or diverges by applving an appropriate test. O P - + + 1 1 : 0 Type here to search рон в резема оо : » Ramna g« E 11:10 PM = - 11/21/2012

Problem 1. Determine whether the following series converges absolutely, conditionally, or diverges (1)k arctan(k) Problem 2 Find the Taylor polynomial P2(x) of x sin12 centered at a = 1 and use it to estimate 1.01(1.01). Problem 3 Give an upper bound on the error term Rs(r) for the Taylor approximation of the function f(x) ln(1-x) on the interval [1/23/2] Problem 4 Find the domain of convergence of the power series (Ink)2 Problem 5 Find a power series expansion of the function ae-, and de- termine its radius of convergence. Problem 6 Find the following limit using Taylor series: lim Tn(1-a) +2 203 PM Type here to search

C Secure https://bbcsulb desire2learn.com d리/le/content/4041/4Menontent 4441 994/View :: Apps D n son Sign In Free Office 365 use f D office Hours Fall 20 Quest n n l ing Assignment 0 Mat Q Rewe Questions C Q o am Design &「 메 Csi 11 7 midterm Fl * Retwr n the nelt (b) Apply an appropriate test to determine whether Σ in converges or diverges n 5. Determine whether the series converges or diverges by applying an appropriate test. 2 6. Determine if the series is absolutely convergent, conditionally convergent, or divergent. If it 7n is convergent, how many terms of the series do we need to add in order to approximate the sum with error0.01? 7. Find the radius of convergence and interval of convergence for the power series Σ(-1)"+13 7n 8. Find a power series representation for f(x) (at 0) and give the interval of convergence ëƒ˜ë‰ 1222 AM Type here to search