5

8_ Show that for every x e Q and every 0 there is a t € I such that If(t) - xl < €. Conclude that f(I) = Q, that is, f is onto Q....

Question

8_ Show that for every x e Q and every 0 there is a t € I such that If(t) - xl < €. Conclude that f(I) = Q, that is, f is onto Q.

8_ Show that for every x e Q and every 0 there is a t € I such that If(t) - xl < €. Conclude that f(I) = Q, that is, f is onto Q.



Answers

Verify each, where $f$ denotes a contradiction. (See Table $1.14 . )$
$$
p \wedge q \equiv q \wedge p
$$

All right. So we want to verify physical relationship. So where we meet. Thank you and you or teeth. So we just need one trip value. This is true. Sure. True. This is false. This is true, true, true. And this is false. So both are equivalent so there's still holds.

Oh okay so you want to verify this? Congratulations ship. So the information we need to know. Not cute. I don't know what that is. I also don't know what and he replies curious and that's what it so final statements this and that's okay so not Q. So this is false too. Oh sure uh P. Implies Q. So if I did something I get something that is true. I did something I didn't get anything that's false. It's something I didn't do something. I got something that is true. I didn't do anything didn't get anything true. And here we have the negation of this statement so that is just falls through false trip. And here we have uh P. And cube. So both of them have had uh the same truth value points of the truth so have not use false. So this is false. Or do they have two values truth? one of those false it's false and one of them is false. It's false.

Okay, So one of our five year statement, so the information we need to know the negation of Q. I also need to know what this conditional statement is being placed, you and I need to know what indication of that is and we need to know what P. And Q is. So the negation of Q false true falls to P implies Q. So you do something, you get something true, you do something but you don't get anything that's false, You don't do something, you get something. Um That is true, You don't do anything, you don't get anything sure. And here the negation of their statements will be false true, you have false false P and Q. So not use false, so this is false. Both of them are true. one of them is false. one of them is false. As you can see, these two statements are identical. So the equivalent relationship holds

F G and Cure polynomial. Is that satisfied? This equation here for all exes except when Q A zero. And then we'd like to go ahead and show that F equals G for all ex. So here, I guess. Case. One. No way should consider, but it's kind of a silly case here. This is a Q is just the zero polynomial. So let me go ahead and put this bar here. So this is his cues. It's not like you've X's hero for some X. It's zero for every ex. So if this is true, then this we automatically have a people's G because we'LL never find an example in which F is not equal to G for some X satisfying. Q. Thanks not equal to zero because this can't happen because he was always zero. So in that case, it's vacuous. Lee Truth. There's really nothing to show then. The second case is Kyu is only zero for some X. So for finally, many exes, a polynomial could have on ly finally, many zeroes. So it's either always zero are on ly zero finally many times. So now if, for example, if Q of A is not equal to zero Then we can use this equation up here and we have enough of a over Cuba Guia que es. Since Cuba is non zero, we can just cancel these and then we see f of a equals jia come So a satisfies this equation here at those a values f equals gene. Now suppose that queue of a does equal zero This is what we'Ll have to use the continuity and that's what the hell is suggesting. So if ave this's weaken right, this is a limit as X approaches a f of x this's by continuity of f f is continuous because it's a polynomial This is given So then we can, right? This is the limit His ex approaches a of genomex So this is of course, when that satisfies this equation here can be zero in the denominator. No. So again, we have to make this assumption here. If we want this last equation now, using continuity of G, we can write this last expression Is she of eh using continuity of G. So this is because ji is continuous. But here's what we shown we shown for any hey whether queue of a zero or not. We always have equals G. So this shows that vehicle's G for all ex values, and that's your final answer.


Similar Solved Questions

5 answers
1 } 1 7 0 1 1 {1 1 L } 1 ;17
1 } 1 7 0 1 1 { 1 1 L } 1 ; 1 7...
5 answers
Considcr the reaction_Alaq) = 3 B(aq)Ke = 5.49x 10-6So0 KIf a 2.80 M sample of A is heated to 500 K. what is thc concentration of B at equilibriumIB|
Considcr the reaction_ Alaq) = 3 B(aq) Ke = 5.49x 10-6 So0 K If a 2.80 M sample of A is heated to 500 K. what is thc concentration of B at equilibrium IB|...
5 answers
1) Let F(x) = 2x2 + 5 and G(x) = 3x2 + 4x 1. Find the following Jur F(-3) Kdeaco PF0G(-k)
1) Let F(x) = 2x2 + 5 and G(x) = 3x2 + 4x 1. Find the following Jur F(-3) Kdeaco PF0 G(-k)...
5 answers
Give & reason for your answer to the following question.Is 84 divisible by 14?Yes, because 84 = 14 . 7.Yes, because 84 = 14 : 6. 14 Yes, because 6 = 84No, because 14 is not a divisor of 84.No, because 84 Is not a multiple of 14
Give & reason for your answer to the following question. Is 84 divisible by 14? Yes, because 84 = 14 . 7. Yes, because 84 = 14 : 6. 14 Yes, because 6 = 84 No, because 14 is not a divisor of 84. No, because 84 Is not a multiple of 14...
5 answers
For 0s05- Ine poldtounded Ine cono 2 =2 Zr and Ira solld boundod anmbo Qid 42-2 havethr cameihieo Which objecihas the greater mass the density - both abjects = p(r,0.z) = Which objeclhus thu greater mass? Sulect tne corect choce Eelow and Ihe ansur Doxu complete choke (Uypo Ox0cI oneute uaing naednoT Paca and netsaMe heiahiaen mnetthu nulbouidIargor Tha mbss 0/ Vie parabeloiThe mat ol Inuconleiu udeaIho colouruui Thu (7105 ytiu cunuMiu MIE > ollliy putubuluu
For 0s05- Ine poldtounded Ine cono 2 =2 Zr and Ira solld boundod anmbo Qid 42-2 havethr cameihieo Which objecihas the greater mass the density - both abjects = p(r,0.z) = Which objeclhus thu greater mass? Sulect tne corect choce Eelow and Ihe ansur Doxu complete choke (Uypo Ox0cI oneute uaing naedno...
5 answers
Determine which of the following statements are tautologies by constructing truth table. Write yes Or not in the space provided. Justily your answers.Iv ~Ib) I-~(vy-(kay~Ip v 9 + (~P^ ~q
Determine which of the following statements are tautologies by constructing truth table. Write yes Or not in the space provided. Justily your answers. Iv ~I b) I-~ (vy-(kay ~Ip v 9 + (~P^ ~q...
5 answers
DueAaLng Cave (rr Icllomnovit4 D074roelon _ JOritiorEElaeJoMAHAI,dixnbutlanL1J6 Lni 1,17911161,17USe saltLrJlatcs "ilh FIEin Wad KLatdo d deviricn #Ex] And InC @tn7 Vn; 231ieenip € Fnc-Iru dotatun $ (Fjund |our A Varehto fou Ucltycanacnfdance InteealWtTa 0acri } _VeDi Veu MitJt"e Unen Ianol JJial ulnt { utreWe
due AaLng Cave (rr Icllomnovit4 D 074roelon _ JOritior EElae JoMAHAI, dixnbutlan L1J6 Lni 1,179 1116 1,17 USe salt LrJlatcs "ilh FIEin Wad KLatdo d deviricn #Ex] And InC @tn7 Vn; 231i eenip € Fnc-Iru dotatun $ (Fjund |our A Varehto fou Uclty cana cnfdance Inteeal WtTa 0acri } _ VeDi Veu M...
5 answers
Question 3A 0.670 kg ball is attached vertically to a spring with a spring constant of 8.00 N/m: The wooden block is pulled down from rest anc then released. What is the initial amplitude of oscillation if the ball's amplitude of oscillation is decreased to 4.40 cm after 31.0 oscillations and the time constant is 33.9 s?0.435 m 0.101 m 9.90 m 0.0192 m
Question 3 A 0.670 kg ball is attached vertically to a spring with a spring constant of 8.00 N/m: The wooden block is pulled down from rest anc then released. What is the initial amplitude of oscillation if the ball's amplitude of oscillation is decreased to 4.40 cm after 31.0 oscillations and ...
5 answers
Using the Second Derivative Test In Exercises $31-42$ , find all relative extrema. Use the Second Derivative Test where applicable.$$f(x)=-x^{3}+7 x^{2}-15 x$$
Using the Second Derivative Test In Exercises $31-42$ , find all relative extrema. Use the Second Derivative Test where applicable. $$ f(x)=-x^{3}+7 x^{2}-15 x $$...
5 answers
A radio antenna 85 feet high is located on top ofan office building: At a distance AD from the base of the building, the angle of elevation to the top of the antenna is 26" and the angle of elevation to the bottom of the antenna is 16" Find the height of the building:26' 416"
A radio antenna 85 feet high is located on top ofan office building: At a distance AD from the base of the building, the angle of elevation to the top of the antenna is 26" and the angle of elevation to the bottom of the antenna is 16" Find the height of the building: 26' 416"...
5 answers
Encrypt the follwowing using RSA, then decrypt the result plaintext =N cipher text=?? ifyou know p=17 9=11 e =7
Encrypt the follwowing using RSA, then decrypt the result plaintext =N cipher text=?? ifyou know p=17 9=11 e =7...
5 answers
19acquicd IniormalanNoE Jlull-DArt queson Once JultsLi {uomdcd u siutui TCLM(0 [S Do Amodei lor tne numzer Lrol jbslerz cuuoml per Ye0i Adasen eumpiidn tmali = MlAf Cif Kren Louane neninn Qrtn Qumbcr ciuorini JieyCUS YejisIde nit~ddoo. cbsler Cet LeJjun in{28ZCODDO Mclc caughlinvear#joclc CnnktULotca }Ihcoconzu-InIBCdoojJRoono~ljcocoxi Tn 7ocodc >Rocjoc?Izi - Nucowon{8880E
19 acquicd Iniormalan NoE Jlull-DArt queson Once JultsLi {uomdcd u siutui TCLM(0 [S Do Amodei lor tne numzer Lrol jbslerz cuuoml per Ye0i Adasen eumpiidn tmali = MlAf Cif Kren Louane neninn Qrtn Qumbcr ciuorini JieyCUS Yejis Ide nit ~ddoo. cbsler Cet LeJjun in{28 ZCODDO Mclc caughlinvear #joclc Cnn...
5 answers
Gruph_the_salotian set of the system of linear inequalities 3yt420 42x410 Y2o
Gruph_the_salotian set of the system of linear inequalities 3yt420 42x410 Y2o...
5 answers
Question 40ZpnAlctt tube I5 Inoculated wvllh 1CO cells 0t 4 bactcrin strain that hxs > Gencration tinc ot 310 minutesThe currylng; Cipaclay Ilic test tube lor Ints strin k billior cells What will the bicterial populatian be alter munutc: Orcutunn;CcnnQueston 412 ptsExponcntial gronth ol # populution _only ParudmenarcustDtut{nc: hremutok recroducrt ( Colronnnur l40ay[ Occui (C CunyunilthDuununctDalbleulcaloll MinEok @ckInun * eded"PmdouoahnngSile #uacln #
Question 40 Zpn Alctt tube I5 Inoculated wvllh 1CO cells 0t 4 bactcrin strain that hxs > Gencration tinc ot 310 minutesThe currylng; Cipaclay Ilic test tube lor Ints strin k billior cells What will the bicterial populatian be alter munutc: Orcutunn; Ccnn Queston 41 2 pts Exponcntial gronth ol # p...
5 answers
Determine if the series converges or diverges; if the series converges, find its sum_3+4 " 7n-1 Converzes; 41 Converzes; 63 Converzes; 47 Diverges
Determine if the series converges or diverges; if the series converges, find its sum_ 3+4 " 7n-1 Converzes; 41 Converzes; 63 Converzes; 47 Diverges...
5 answers
HistontBookrarksFEdOIWindou35*07 Sat 7310 PMaJUserskmolznoorali Downloads 28k20Group%2ActivltyYouuboNdntSolaonngUrienmcame45 5151acltalio UodcnWnnahoyalty Free LoopDanto6.2 GrQup ActivityRefer the figure and fnd the volume gencrated by rotating the given region about the given lineCiu8(8.2130 47 Yt %t Y-about OAStv about OCabout ABabout BCabout OASlz about OC'
Histont Bookrarks FEdOI Windou 35*07 Sat 7310 PMa JUserskmolznoorali Downloads 28k20Group%2Activlty Youubo Ndnt Solaonng Urien mcame 45 5151 acltalio Uodcn Wnna hoyalty Free Loop Danto 6.2 GrQup Activity Refer the figure and fnd the volume gencrated by rotating the given region about the given line ...
5 answers
6. Use the Direct Comparison Test to determine the convergence or divergence of the series:C05n Cm-0 6n+6
6. Use the Direct Comparison Test to determine the convergence or divergence of the series: C0 5n Cm-0 6n+6...

-- 0.022175--