## Question

###### (a) State and prove the theorem giving the Weierstrass M-test. You may use the Cauchy convergence criterion without proof:[10](b) Consider the functional series Li (c â‚¬ (1,0)) J=] Given the information that the functional series (*) is pointwise convergent, show that it is uniformly convergent on [@, 0o) for each (ii) Show that the formally differentiated series (obtained by differentiating term by term) is uniformly convergent on [a,0) for each You may use without proof the inequality j Fa /

(a) State and prove the theorem giving the Weierstrass M-test. You may use the Cauchy convergence criterion without proof: [10] (b) Consider the functional series Li (c â‚¬ (1,0)) J=] Given the information that the functional series (*) is pointwise convergent, show that it is uniformly convergent on [@, 0o) for each (ii) Show that the formally differentiated series (obtained by differentiating term by term) is uniformly convergent on [a,0) for each You may use without proof the inequality j Fa / log j < where exp(1) ea (iii) Use the results of and to show that the function ((z) Lj [15] (c â‚¬ (1,00)) is continuously differentiable-

## Answers

#### Similar Solved Questions

5 answers

##### ReviewPant AA parallel-plate capacitor is formed from two 3.5 cm diameter electrodes spaced 0 mm apart The electric field strength inside the capacitor is 2.0 X106 N/C You may want to review (Pages 644 - 645)What is the charge (in nC) o each electrode? Express your answer using two significant figuresAZdnCSubmitRequest AnswerProvide Feedback

Review Pant A A parallel-plate capacitor is formed from two 3.5 cm diameter electrodes spaced 0 mm apart The electric field strength inside the capacitor is 2.0 X106 N/C You may want to review (Pages 644 - 645) What is the charge (in nC) o each electrode? Express your answer using two significant fi...

5 answers

##### 2,0.10 4 [ 1 1 1Tale Win cuch _Utu increase U 4unos 0 K 1 4conducied1

2,0.10 4 [ 1 1 1 Tale Win cuch _Utu increase U 4unos 0 K 1 4conducied 1...

5 answers

##### Large metropolitan 21) The following data represent the living situation of newlywedsin = aree and their annual household income Find the marginal frequencies 0oO S50-75,000 3575 OoO <$20,000 S20-35,000 535-50_ 355 524 202 Own home 23 11 52 Rent home 30 Live w/family]

large metropolitan 21) The following data represent the living situation of newlywedsin = aree and their annual household income Find the marginal frequencies 0oO S50-75,000 3575 OoO <$20,000 S20-35,000 535-50_ 355 524 202 Own home 23 11 52 Rent home 30 Live w/family]...

5 answers

##### Large organisation has been accused of being ageist'= tending people: In not to response, it publishes thc employ older following = table employees: showing the age distribution of its currentAge last birthday (years) 15 _ 19 20 _ 24 25 _ 29 30 _ 39 40-49Number of cmployees 240 340 360420 380 24050 - 64Draw histogram to show thc age distributionState, with reasons, whether the data suggest that the organisation is ageist.Explain why the way the data have been presented in the table may the

large organisation has been accused of being ageist'= tending people: In not to response, it publishes thc employ older following = table employees: showing the age distribution of its current Age last birthday (years) 15 _ 19 20 _ 24 25 _ 29 30 _ 39 40-49 Number of cmployees 240 340 360 420 38...

5 answers

##### Fk)- 8 1.If lim = 10, X-1 X-1find lim f (x) X71

fk)- 8 1.If lim = 10, X-1 X-1 find lim f (x) X71...

5 answers

##### (1point ) [Old Exams] lim f(r) and lim f(r) both exist, but lim f(r) What is the type of discontinuity wherc does not exist?lim f(c) - g(c) lim f(z) and lim f(c) exist, but ncither Give example where lim f(r) nor lim ,9(r) exists (Hint: Draw two graphs for an educated guess. Then give the rules of two piecewise defined functions and their sum

(1point ) [Old Exams] lim f(r) and lim f(r) both exist, but lim f(r) What is the type of discontinuity wherc does not exist? lim f(c) - g(c) lim f(z) and lim f(c) exist, but ncither Give example where lim f(r) nor lim ,9(r) exists (Hint: Draw two graphs for an educated guess. Then give the rules o...

5 answers

##### Q1. SHOW ALL WORK TO GET POINTS This includes drawing the Lewis Structure Consider the following molecule: nitrogen tribromide_ NBrz-Draw Ihe best Lewis structure_ What the molecular geometry of the compound above? What bond angles do you expect? Whal is the hybridization state ol the central alom? Is this polar molecule? What type of intermolecular forces the above compound have with itseli?02.Show ALL WORK TO GET POINTS * This includes drawing the Lewis Structure Answer the questions for the f

Q1. SHOW ALL WORK TO GET POINTS This includes drawing the Lewis Structure Consider the following molecule: nitrogen tribromide_ NBrz- Draw Ihe best Lewis structure_ What the molecular geometry of the compound above? What bond angles do you expect? Whal is the hybridization state ol the central alom?...

5 answers

##### ASuOOsaJ Sil] #AES mim Uoilsanb Jalioue 01 SuvoWJOozh {ojzh zo) EOjH(bp ) HO + (bp ) â‚¬ OJH + (bo )-z 803 + 6Joz Huoipeaj Bujmollo} ay1 UI pije KMo7-pazsuoug a41 Kynuapiuoins3n6

aSuOOsaJ Sil] #AES mim Uoilsanb Jalioue 01 SuvoW JO ozh {ojzh zo) EOjH (bp ) HO + (bp ) â‚¬ OJH + (bo )-z 803 + 6Joz H uoipeaj Bujmollo} ay1 UI pije KMo7-pazsuoug a41 Kynuapi uoins3n6...

5 answers

##### V3 Pointe]DETAILSPREWOUS ANSWERSOSCOLPHYS2016 17.6.P.057.Lht dosest lrequrnolJvenau Dlison â‚¬ crat dstingutsh UennoeeuaaerenAller uequoncylarge lequcncy

V3 Pointe] DETAILS PREWOUS ANSWERS OSCOLPHYS2016 17.6.P.057. Lht dosest lrequrnol Jvenau Dlison â‚¬ crat dstingutsh Uennoeeuaaeren Aller uequoncy large lequcncy...

5 answers

##### 28)If V = 20 V and thc battery is ideal, whal is the current through R3 in the figure? 10 (2R; = Z0(LZuILHa

28)If V = 20 V and thc battery is ideal, whal is the current through R3 in the figure? 10 (2 R; = Z0(L ZuIL Ha...

5 answers

##### Is Ohm $ Law satisfied for the circuit as a whole? Think about this by using the battery voltage and the current coming from the battery. What total resistance does Ohm's Law suggest the circuit has as a whole? How is this total resistance related to R; and Rz and R; Explain:RTatal (write a numerical value here based on the battery voltage and the current from the battery)RIotal (write an equation in terms of R,, Rz and R;)I

Is Ohm $ Law satisfied for the circuit as a whole? Think about this by using the battery voltage and the current coming from the battery. What total resistance does Ohm's Law suggest the circuit has as a whole? How is this total resistance related to R; and Rz and R; Explain: RTatal (write a nu...

5 answers

##### 7a84i8i44ff 8 HI V 0 & : @ : 1 J 1 { 1 3 1 1 3 | L 7 3 ! 1 1 L

7a84i8i44ff 8 HI V 0 & : @ : 1 J 1 { 1 3 1 1 3 | L 7 3 ! 1 1 L...

5 answers

##### Evaluate the following: T 2 0 Jo Joos esin 0 drde

Evaluate the following: T 2 0 Jo Joos esin 0 drde...

5 answers

##### Solve the absolute value equation and graph the solution on the real number line.$$|x|=5$$

Solve the absolute value equation and graph the solution on the real number line. $$|x|=5$$...

5 answers

##### A given peak of a wave travels 35 meters in 12 seconds, but when concentrating only one particle in a wave, you find that it completes 7.4 cycles in 15.2 seconds, what is the wavelength of the wave? (5 marks)

A given peak of a wave travels 35 meters in 12 seconds, but when concentrating only one particle in a wave, you find that it completes 7.4 cycles in 15.2 seconds, what is the wavelength of the wave? (5 marks)...

5 answers

##### EL 4 volum& aE_ 4e SJGd s fust_actant bounda 6y Cyladec 2= Leax and # planx 425

EL 4 volum& aE_ 4e SJGd s fust_actant bounda 6y Cyladec 2= Leax and # planx 425...

4 answers

##### A study found that the trans fat content in fast-food products varied wldely around the world, based on the type of frying oil used as shown in Ihe table; Ihe set of countries is Ihe domain and Ihe set ol trans fal percentages is (he range ol (he functlon consisting of the six pairs listed , is the function one-to-one function?Percentage of Trans Fat in Country fast-food products Country A Country B Country C Country D Country E Country FIs the function a one-tO-one function?NoYes

A study found that the trans fat content in fast-food products varied wldely around the world, based on the type of frying oil used as shown in Ihe table; Ihe set of countries is Ihe domain and Ihe set ol trans fal percentages is (he range ol (he functlon consisting of the six pairs listed , is the ...

5 answers

##### How would you expect cardiac muscle tissue to look differentthan the skeletal muscle tissue you observed? How would you expectsmooth muscle tissue to look different than the skeletal muscletissue you observed?describe the components shown in the labeled cartilage diagramyou observed in the Procedures.describe the components shown in the bone image you observed inthe Procedures

how would you expect cardiac muscle tissue to look different than the skeletal muscle tissue you observed? How would you expect smooth muscle tissue to look different than the skeletal muscle tissue you observed? describe the components shown in the labeled cartilage diagram you observed in the Proc...

5 answers

##### Atcrc nranin) CnanT COS(d)43 5c^ # . ( =51}Circle one: Absolutely convergentConditionally convergentDivergentWhyltest(s)?

atcrc nranin) Cna nT COS (d) 43 5c^ # . ( = 51} Circle one: Absolutely convergent Conditionally convergent Divergent Whyltest(s)?...

5 answers

##### 1 8 1 8 I 3 1 ] 2 1 3 Wu 1 Wi 1 I 1 iwl Ww { 0 V 8 HHH X! 8 8 8 8 9 1 2 2 9 2 9 1 8 1 3 1! 3 < 1 3 0! { M91 1 01 1 8 I1 1

1 8 1 8 I 3 1 ] 2 1 3 Wu 1 Wi 1 I 1 iwl Ww { 0 V 8 HHH X! 8 8 8 8 9 1 2 2 9 2 9 1 8 1 3 1! 3 < 1 3 0! { M91 1 01 1 8 I 1 1...