Math32B_midterm2solutions

# Math32B_midterm2solutions - Friday 2/22 MATH 3113 A...

This preview shows pages 1–5. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Friday 2/22 MATH 3113 A oémeiilz (if C Last name : First name : Section -. UCLA ID number : Signature : Instructions : full credit will be given only if your solution is given with all the details. Notes and calculators are not allowed. CREDIT ; SCORE : Problem l :10 points Problem 2 :10 point-S Problem 3 :20 point-e Problem 4 :10 points TOTAL : 40 points DER : cosgw +Sin2\$ : 1. seegzr a 1 + ten2 :3. (i i a"; (arctan) z w. Comparison theorem. Consider two positive functions 0 S S on an interval I. Then, f{:r)d.:r. convergesl implies [f1 g{3:)dz converges]. in) g(;e)d:r divergesl implies [f] f{\$)dcc diverges]. Absolute c0nvergence. converges] implies f(:c)d\$ converges]. Probiem Find f < 1, 3x2 +2\$+3 d3 2: +1){m2 +1) 35%»: “A ms gﬁﬁ‘ ? a”) gmgv .g ,2 ma EWan 4 5:: M £3; 9%?“ j \$53415 “WM walem ’2. Find 1 ah. I \$4 “xi-\$2 +1 a :Ezgfswmgw «w 1: 3mm 5 y 3% gym? 65\$ 57 j £235“ «:2 ﬂag: as; f r <5 2* f3?» ‘1. ii Ami? {£53 a. jig? (£25; 1 r WW :2: M M j; 5%? ﬁg; ‘ 5%? 4 “’3 g aw in.“ { éxf M 5359;? {(55% j 3*“ 553' WVW“ Sgh§ 25) (iii '2 w§ .‘3 ,_ 2 agﬁﬁé: asaﬁﬁfw’: 5”)” .5; 4 g fMﬁf/Q r: M I" g; c552”: ﬁmwzigﬁh ﬁery @ jig-ﬁg ﬁg: M m» 9.» mg; + 3 \$5: Probiem 3. (You are not asked :0 ﬁnd the vaiue) a) Preve that I; 3mm J31"- dx converges. b} Prove that fix gigs—gait canverges‘ S‘MK < ai Q g M“ “‘ g; w; Z él “‘ £3) a g ’5’ i?§€ «Pg-2‘3 w {- Q g“ Q 0% C?" a? éﬂi f “1 cm L 5% i VSMX {gt CV LG? 2 m M 5 i%%g Thaw/9“; Probiem +OD ta—l Cﬂnsider the fmmtion [1(a) 2 a (if 1 + t “ a} Prove that H(a) converges for D < a < 1. b) W'hat. is Hﬂ/Q). c) Prove that HQ A a) : H(a), Va E (0,1). a} X, fféwﬁﬁ : «4 , j 5,: ﬂ 5:: WP :aﬁf 0/5” {E}; C: 6’ (i/ 5" 2M Mg: ass—vi 4 90\$ rf’va s\$éﬂ é? (fa «- Mai ﬂ 15,5? g .1... G \$0» aw: i} 1/,” {Law} 45/ 5+5?- f 4/ my- 1 ma “ £5; CV mg. iw>i 7»; they} CV 14;; 9’ 95;. ,4; a: W: «\$4629 r“ J :1 W Q 34-5/5?” i} ggswifﬁww H, j . . M W? ’36 y '3 fwd-a V3}: {fig ...
View Full Document

## This note was uploaded on 10/27/2008 for the course MATH 32B taught by Professor Rogawski during the Winter '08 term at UCLA.

### Page1 / 5

Math32B_midterm2solutions - Friday 2/22 MATH 3113 A...

This preview shows document pages 1 - 5. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online