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### 242hw6

Course: MATH 242, Spring 2011
School: Delaware
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Word Count: 147

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242 Math Homework 6 Sections 012 and 014: Due Wednesday March 23rd Section 050: Due Tuesday March 22nd Questions 1 through 5 should be done by hand. For questions 6 through 8, you can use Maple as much or as little as you like. 1. Evaluate sin(ln x) dx. (May be a little tricky.) 2. Evaluate x2 0 x dx or show that it is divergent. +2 3. Use Newtons Method to nd a good approximation to 99991/4 . 4. Find the...

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242 Math Homework 6 Sections 012 and 014: Due Wednesday March 23rd Section 050: Due Tuesday March 22nd Questions 1 through 5 should be done by hand. For questions 6 through 8, you can use Maple as much or as little as you like. 1. Evaluate sin(ln x) dx. (May be a little tricky.) 2. Evaluate x2 0 x dx or show that it is divergent. +2 3. Use Newtons Method to nd a good approximation to 99991/4 . 4. Find the length of the curve = y ln(sec x) between x = 0 and x = /4. 5. Find the length of the curve y = ln(1 x2 ) between x = 0 and x = 1/2. 5 cos x dx using both the Trapezoid Rule and Simpsons Rule x 1 with n = 8, n = 16, and n = 32. 6. Estimate 1 7. Estimate 2 ex dx using both the Trapezoid Rule and Simpsons Rule 0 with n = 4 and n = 10. 8. Use Simpsons Rule with n = 10 to estimate the length of the curve y = xex between x = 0 and x = 5. 1
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Delaware - MATH - 242
Math 242 Homework 6Solutions (to the by hand questions)Questions 1 through 5 should be done by hand.For questions 6 through 8, you can use Maple as much or as little as you like.1. Evaluatesin(ln x) dx. (May be a little tricky.)Solution. Let I =sin
Delaware - MATH - 242
Math 242 Homework 7Sections 012 and 014: Due MONDAY April 11thSection 050: Due Tuesday April 12thIn questions 1 through 8, determine whether the series converges or diverges.(Give reasons.)1.1n=1 2n2.lnn=1n2 + 12n2 + 13.1 + 3n2nn=14.nn
Delaware - MATH - 242
Math 242 Homework 7SolutionsIn questions 1 through 8, determine whether the series converges or diverges.(Give reasons.)1.n=112nSolution. This series is2.lnn=11times the harmonic series, so it diverges.2n2 + 12n2 + 1n2 + 11Solution. Not
Delaware - MATH - 242
Math 242 Homework 8Sections 012 and 014: Due Wednesday April 20thSection 050: Due Tuesday April 19thIn Questions 1 to 4, determine whether the series converges or diverges. Givereasons.1.n1nn=1 n 4(1)n sin2.n=1n3.1 + sin n10nn=14.nn3 +
Delaware - MATH - 242
Math 242 Homework 8Solutions (may be somewhat terse)In Questions 1 to 4, determine whether the series converges or diverges. Givereasons.1.n1nn=1 n 4n11 n = n , or limitCONVERGES. Try basic comparison with bn =n44comparison with the same bn
Delaware - MATH - 242
Math 242 Homework 9Sections 012 and 014: Due Wednesday April 27thSection 050: Due Tuesday April 26thIn questions 1 to 5, nd the interval of convergence of the power series.1.xn3n=1 n2.nxnn=13.xnnn=2 4 ln n(1)n4.n=05.(1)nn=0x2n(2n)!(
Delaware - MATH - 242
Math 242 Homework 9Solutions (may be somewhat terse)In questions 1 to 5, nd the interval of convergence of the power series.1.n=1xnn3an+1xn+1n3n3= n = |x| |x|. So |x| &lt; 1. Checkingan(n + 1)3 x(n + 1)3endpoints, we nd that both are includ
Delaware - MATH - 242
Math 242 Homework 10Sections 012 and 014: Due Wednesday May 4thSection 050: Due Tuesday May 3rdex 1dx as a power series.x1. Express the indenite integral0 .21dx as an innite series.1 + x50Then nd the sum of the rst two terms of that series. Co
Delaware - MATH - 242
Math 242 Homework 10Solutionsex 1dx as a power series.x1. Express the indenite integralxx2 x3 x4e =1+ ++++ 1!2!3!4!xx2 x3 x4x+++ e 1= +1!2!3!4!xex 11xx2 x3=+++ x1! 2!3!4!xx2x3x4ex 1dx =++++ x1 1! 2 2! 3 3!
Delaware - MATH - 242
Math 242 Homework 11Sections 012 and 014: Due MONDAY May 9thSection 050: Due Tuesday May 10th1. Consider the parametric curve x = t + ln t, y = t ln t, where 0 &lt; t &lt; .Find dy/dx and d2 y/dx2 . Find where the curve is increasing, decreasing,concave up
Delaware - MATH - 242
Brief solutions for (parts of) Homeworks 3 and 4Homework 4 /6 /6300= uu332. I =1/2=0(1 u2 ) du(1 sin x) cos x dx =cos x dx =1.sin /62sin 01111=.2 2424sec3 x dx =sec x sec2 x dx. Integrate by parts with u = sec x,dv = sec2 x dx
Delaware - MATH - 242
Math 242 Review Part 1In this course, we covered most of the following four chapters. Chapter 6 (Applications of Integration) Chapter 7 (Techniques of Integration) Chapter 11 (Innite Series) Chapter 10 (Parametric and Polar Curves)There were three a
Delaware - MATH - 242
Math 242 Review Part 2In addition to (most of) Chapters 6, 7, 11, and 10, we studied the followingthree miscellaneous topics: Newtons Method (4.8) LHopitals Rule (4.4) Arc Length (8.1)1. Use Newtons method with the specied initial approximation x1 t
Delaware - MATH - 242
Math 242Suggested lab/discussion problems, Sept 6 and 81. Evaluate lim x1/x .x12. Evaluate xlim ( x2 + x x).23. Evaluate(3x 2)20 dx.34. Evaluatesin t dt.4
Delaware - MATH - 242
Math 242Suggested lab/discussion problems, Sept 13 and 151. Find the area bounded by the curves y = x2 and y =1x22.+12. Find the area bounded by the curves y = |x| and y = x2 2.23. Let R be the region bounded by the curves y = 1 x2 and y = 0. Fi
Delaware - MATH - 242
Math 242Suggested lab/discussion problems, Sept 20 and 221. Let A be the region bounded by y = ex , y = 1, and x = 2. Find thevolume obtained by revolving A around the line y = 2.12. Let A be the region bounded by y = 4x x2 and y = 3. Find the volume
Delaware - MATH - 242
Math 242Suggested lab/discussion problems, Sept 27 and 291. Evaluatesin4 x dx.12. Evaluatecos5 x dx.2173. Evaluatexex dx.03 /24. Evaluatesin3 x cos11 x dx.04
Delaware - MATH - 242
Math 242Suggested lab/discussion problems, Oct 4 and 6101. Evaluate4x26dx.911dx.2 + 2xxHINT: Start by completing the square.2. Evaluate213. Evaluatex x2 + 4 dx.034a. Evaluatexdx.x2 + 14b. Evaluatex2dx.x2 + 14
Delaware - MATH - 242
Math 242Suggested lab/discussion problems, Oct 11 and 1321. Use the Trapezoidal Rule and Simpsons rule to approximate0using n = 4 subintervals.11dx1 + x42. Evaluate0(x2xdx.+ 2)223. Find a good approximate root of x3 x 1 = 0 by starting wi
Delaware - MATH - 242
Math 242Suggested lab/discussion problems, Oct 18 and 201. By hand, nd an approximation to 71/3 . Choose an appropriate functionf (x), an appropriate rst approximation x1 , and nd x2 .12. Find the length of the curve y = ln(sec x) between x = 0 and x
Delaware - MATH - 242
Math 242Suggested lab/discussion problems, Oct 25 and 27This is a longer list of problems than usual. It can also serve as practice forTest 2. /21a. Evaluatecos3 x dx.0 /21b. Evaluatecos2 x dx.012. Evaluatesec3 x dx.223. Evaluate1x2 1d
Delaware - MATH - 242
Math 242Suggested lab/discussion problems, Nov 1 and 3D1. Does the series converge or diverge?1nn=1 n + 3D2. Does the series converge absolutely, converge conditionally, or diverge?(1)n+1n=2 n ln n1D3. Does the series converge absolutely, conver
Delaware - MATH - 242
Math 242Suggested lab/discussion problems, Nov 8 and 10D1. Does the series converge or diverge?n2 132n=1 n + 2n + 5xnD2. Find the interval of convergence of the power series.n=0 n!1D3. Find the interval of convergence of the power series(2)n
Delaware - MATH - 242
Math 242Suggested lab/discussion problems, Nov 15 and 17D1. Find a power series representation of the function f (x) =is the radius of convergence of your power series?1. What1 + x2D2. Find a power series representation of the function f (x) = arct
Delaware - MATH - 242
Math 242Suggested lab/discussion problems, Nov 221. Evaluate the integralcos x (1 + sin2 x) dx.2. Evaluate the integralsin3 xdx.cos x113. Evaluate the integral0earctan xdx.1 + x24. Does the series2n n!converge or diverge?n=1 (n + 2)!25
Delaware - MATH - 242
Math 242Suggested lab/discussion problems, Nov 29 and Dec 1converge or diverge? If it converges,nn=1does it converge absolutely or conditionally?(1)n sinD1. Does the seriesnD2. Does the seriesn=123nconverge or diverge?1D3. Does the series
Delaware - MATH - 242
Math 242, U of D, Spring 2011Analytic Geometry and Calculus BInstructor: Idris Mercer, Ewing 529, idmercer@math.udel.eduIn emails, please write Math 242 and your section number.Oce hours: Mondays 5:006:30, Thursdays 9:0011:00, or by appointmentCourse
Delaware - MATH - 242
M ath 242 Section 010: Test #1NAME: _L/CPlease circle your l ab/discussion:020021022This test has 6 questions on 6 pages.The p oints per page are 5, 5, 5, 5, C, 6.Show your &quot;work. A correct answer w ith l ittle or no reasoning may reeeivea low s
Delaware - MATH - 242
M ath 242 Section O il: Test #1NAME: _frPlease circle your lab/discussion:030031032This test has 6 questions on 6 pages.The points per page are 5, 5, 5, 5, G, 6.Show your work. A correct answer with little or no reasoning may receivea low score.
Delaware - MATH - 242
Math 242 Section 012: Tost #1NAME:KEYPlease c ircle y our l ab/discussion: 040 ( 8:00) 041 (12:30) 042 ( 1:30)This t est, has 6 questions on 6 pages.The, p oints per page are 5, 5. 5, .r&gt;, G , fi.Show your work. A correct answer with little or no r
Delaware - MATH - 242
Math 2 42 S uction 0 14: TostN AME:KEYPlease c ircle your l ab/discussion: 060 ( 12:00) 061 (11:00) 062 ( 2:30)This test has 6 questions on 6 pages.The points per page are 5. 5, 5, 5, 6. 6.Show your work. A correct, a nswer with l ittle or no r easo
Delaware - MATH - 242
M ath 242 Section 050: Testi/c:NAME: _(^f^This test has G q uestions on 6 pages.The p oints p er pa^e are 5, 5, 5, 5, ( i, 0.Show y our w ork, A c orrect answer w ith l ittle o r no r easoning m ay r eceivea. low score. (However, there is no need to
Delaware - MATH - 242
Math 242 Section 010: Test #2N AME:Please circle your lab/discussion:020021022This test has 6 questions on 6 pages.The points per page are 5, 5, 5, 5, 6, 6.Show your work. A correct answer w ith little or no reasoning may receivea low score. (How
Delaware - MATH - 242
Math 242 Section 014: Test #2NAME:Please circle your lab/discussion:060061062This test has 6 questions on 6 pages.The points per page are 5, 5, 5, 5, 6, 6.Show your work. A correct answer w ith little or no reasoning may receivea low score. (Howe
Delaware - MATH - 242
Math 242 Section 012: Test #2NAME:Please circle your lab/discussion: 040 (8:00) 041 (12:30) 042 (1:30)There are 6 questions on 6 pages. Points per page: 5, 5, 5, 5, 6, 6.Show your work. A correct answer with little or no reasoning may receivea low sc
Delaware - MATH - 242
M ath 242 Section 014: Test #2NAME:&lt;^ ^ VPlease circle your lab/discussion: 060 (12:00) 061 (11:00) 062 (2:30)There are 6 questions on 6 pages. Points per page: 5, 5, 5, 5, 6, 6.Show your work. A correct answer with little or no reasoning may receive
Delaware - MATH - 242
Math 242 Section 050: Test #2NAME:There are 6 questions on 6 pages. Points per page: 5, 5, 5, 5, 6, 6.Show your work. A correct answer with little or no reasoning may receivea low score. (However, there is no need to be wordy.)The 7th page has some f
Delaware - MATH - 242
Math 242 Section 012: Test #3N AME:KEYPloa.sc c ircle your l ab/discussion: 040 (8:00) 041 (12:30) 042 (1:30)There are 6 questions on 6 pages. Points per page: 5, 5, 5, 0, 5, 6.The 7tli page has some formulas you can refer to if needed.[5 points] Qu
Delaware - MATH - 242
Math 242 Section 014: Test #3N AME:'Please circle your lab/discussion: 060 (12:00) 061 (11:00) 062 (2:30)There are 6 questions on 6 pages. Points per page: 5, 5, 5, C, 5, 6.The 7th page has some f ormulas you eari refer to if n eeded.[5 p oints] Que
Delaware - MATH - 242
M ath 242 Section 050: Test #3NAME:_There are 6 questions on 6 pages. P ointy per page: 5, 5, 5, 0, 5, 6.The 7th page has some f ormulas you can refer to if needed.[5 points] Question 1. D etermine whether the i nfinite seriesis absolutely convergen
Delaware - MATH - 242
TO S OMfcdx.8. Evaluate-x-K/0010-0.6f)0rh.9. Evaluate / ye~-6y dy.JoU'-O.b-0.6Jo10. Evaluate6'~0 -r /2 cos o1 + sinXV~Jo,rffl.U11. Evaluateu=It +=?323UJ:,12. Evaluate /_1/1.\.il:i2shr 0 cos-0 &lt;/0.7ofNTT/2-00U
Delaware - MATH - 242
IDCHf\Pm 7In problems 23 to 28, evaluate the integral or show t hat it is d ivergent.,00,PML23.i'&quot;%'3L\J324.,dxMM25. /f l/audx13r&gt;\?rovooH&gt;-4--V\MvoXr.X\MotocX^-t&lt;xcto4-P\IO4-14:tou]OS
Delaware - MATH - 242
1. Sketch t he curve. Indicate the direction in which the curve is traversed ast increases. If possible, eliminate the parameter to find a Cartesian equationof the curve.la.x = 3i - 5,y = 2t + la+5&quot; - s-tM&quot;3fH1l-1-lb.3.&gt;x = t2 - 2,3(/ =
Delaware - MATH - 242
iitIii questions 1 to 28, d etermine w hether t he series converges or diverges.iooV^ / o-n3-&quot; +1.3/2p-sn?;rsOO-12. V tan-j^vi n1&lt;:.os KIntA-M^1fw^ ^-^ . ^ ~^)3 c osy?,3.77/V2 _ 2q3'^5 AKI ^-2^choose c, ^V)J|c.*I^/ ^/HfCCO
Delaware - MATH - 242
Iii questions 29 to 36, d etermine whether the scries converges absolutely, converges conditionally, ordiverges.n29.3n0&gt;30.J'IJnofisi/In=l5011In questions 37 to 42, find the interval of convergence of the power scries.3. - 2 )/^a-Z
Delaware - MATH - 242
(?ay71/-7CXTOoT7T007X=Y)p~l7._vi /3/3/3-/Wt /i i^.^/ ^3n3&quot;- Ji lt*i^*&quot;-oi&quot;^tA -^oOi&lt;~)~y^,tTi 3 + 5'&quot;)'.-IK00f-i' n5An+1n3/2 - 2rartA/|AI&quot;/6^J=.^_/-x16. V ^n)*17.n siTi1n^W00O Tl/aL,
Delaware - MATH - 242
In questions 1 to 28, determine whether the series converges or diverges.11.3n + 3/2nn=1tan2.n=11n3.3 cos n3/2 2n=1 n14.n=15.n=1132n1+n1ln(n + 1)6.1n=2 n(ln n)27.1n=2 n ln n8.12n=2 n(ln n)9.12n=2 (ln n)310.1n=
Delaware - MATH - 242
The last page of your test will contain exactly these formulas in exactly thisformat.sin2 x =11 cos 2x2cos2 x =11 + cos 2x21dx = ?1 + x2sec x dx = ln | sec x + tan x| + C1+x2 x3x+++ = ?1!2!3!xx 3 x5 x7++ = ?3!5!7!1x 2 x4 x6
Delaware - MATH - 242
Review for beginning of Math 242This document covers some topics that you should have learned in Math 241or whatever your equivalent course was.If x = 3, evaluate x2 , x2 , 2x2 , and 2x2 .If x = 3, evaluate x2 , x2 , 2x2 , and 2x2 .Expand and simplif
Delaware - MATH - 242
Strategy for testing seriesWe skipped Section 11.7, which is very short and contains some strategyfor testing series. Heres my version of that strategy.STEP 0. Does the nth term an approach 0? If it doesnt, then the seriesdiverges. (I think of this as
Delaware - MATH - 242
INFINITE SERIES (Chapter 11)General facts:A sequence is nothing but an innite list. A series is a sum of innitely many numbers.An innite series may either converge (i.e. reach a nite total) or diverge (i.e. not reach a nite total).1A famous example o
Delaware - MATH - 242
This page has some formulas that will NOT be given on your test.You will probably want to memorize these formulas, and also understandwhen and how they are used.This is an INCOMPLETE list of SOME things you will need to know. R2 r2 dxVolume by washer
Delaware - MATH - 242
This page is not part of your test.It contains some formulas you may nd useful.Note that some formulas contain blanks.You should know how to ll in the blanks, but you are not required to llthem in explicitly.sin cos tan 0/6/4/3/2dsin x =dx
Delaware - MATH - 242
This page is not part of your test.It contains some formulas you may nd useful.Note that some formulas contain blanks.You should know how to ll in the blanks, but you are not required to llthem in explicitly.sin cos tan 0/6/4/3/2sin2 x =11
Delaware - MATH - 242
Math 242Suggested lab/discussion problems, Oct 25 and 27This is a longer list of problems t han u sual. It can also serve as pract.iec forTest 2.r1'2 cosla. Evaluate /,rr/21x dx.7O\$ 2 / X COS ^o^6(A ' S'^ ^/-COSIb. Evaluate /o,cos x dx
Delaware - MATH - 242
This page is not part of your test.It contains some formulas you may nd useful.Note that some formulas contain blanks.You should know how to ll in the blanks, but you are not required to llthem in explicitly.sin2 x =11 cos 2x2cos2 x =11 + cos 2
Delaware - MATH - 242
Math 242 Section 014: Test #1NAME:Please circle your lab/discussion: 060 (12:00) 061 (11:00) 062 (2:30)This test has 6 questions on 6 pages.The points per page are 5, 5, 5, 5, 6, 6.Show your work. A correct answer with little or no reasoning may rece
Delaware - MATH - 242
Math 242 Section 012: Test #1NAME:Please circle your lab/discussion: 040 (8:00) 041 (12:30) 042 (1:30)This test has 6 questions on 6 pages.The points per page are 5, 5, 5, 5, 6, 6.Show your work. A correct answer with little or no reasoning may recei
Delaware - MATH - 242
Math 242 Section 050: Test #1NAME:This test has 6 questions on 6 pages.The points per page are 5, 5, 5, 5, 6, 6.Show your work. A correct answer with little or no reasoning may receivea low score. (However, there is no need to be wordy.)The 7th page
Delaware - MATH - 242
Math 242 Section 014: Test #2NAME:Please circle your lab/discussion: 060 (12:00) 061 (11:00) 062 (2:30)There are 6 questions on 6 pages. Points per page: 5, 5, 5, 5, 6, 6.Show your work. A correct answer with little or no reasoning may receivea low s
Delaware - MATH - 242
Math 242 Section 012: Test #2NAME:Please circle your lab/discussion: 040 (8:00) 041 (12:30) 042 (1:30)There are 6 questions on 6 pages. Points per page: 5, 5, 5, 5, 6, 6.Show your work. A correct answer with little or no reasoning may receivea low sc