a-find-the-approximations-t_10-and-m_10-for-int_12-e1-x-d-x-b-estimate-the-errors-involved-in-the-ap

Question

(a) Find the approximations $T_{10}$ and $M_{10}$ for $\int_{1}^{2} e^{1 / x} d x$
(b) Estimate the errors involved in the approximations of
part (a).
(c) How large do we have to choose $n$ so that the approxi-
mations $T_{n}$ and $M_{n}$ to the integral in part (a) are accu-
rate to within 0.0001$?$

Jiji Peter · Accepted Answer

for ricin 18 6 20 using the rule or integration from one to do yeah to the power one over X, d X and in equals 10. Does the X the woods off interval with equal to minus 1/10? It will go, went one. Then we conclude the values at the interval. Boundaries for F X equal. Mhm, the power one over X and each X. We will find the value if it&#x27;s at X equal one. Fix it going. Seven. Wow! And it&#x27;s equal 1.1. It takes equal 2.48 at X equal. One way to fix equal 2.3 and etcetera still X equals two. If X would be equal 1.64 Hey! And we right out of the refrigerator rule for in the plasma at our condition. 11 terms and they feel in the numbers of from the table through de 10. With equal. There&#x27;s the X for over to off the blind boy If exports plus who, if it&#x27;s one lost to If the accessory etcetera, then to if it&#x27;s night loss. If it&#x27;s again by director institution, we will find the value off teeth and equal 2.2 19 76 Using the midpoint toe, we calculate the values at the mid points off each interval. At the checks, we will get the value off you&#x27;re fixed, you will get the value of X equals 1.5 Sorry x equal Ongoing 05 to fix equal 2.59 at X equals 1.15 If a sequel don&#x27;t work 38 at X equal one going to five if X equal, Don&#x27;t worry total and etcetera till X equal 1.95 to fix equal one Brain 66 nine For the midpoint rule we multiplies of its off. Each interval tells the X Times is a some off each fx upon the midpoint table. So in with him it won the X off the Blind Boy if in one plus it&#x27;s a me too glass, if a mystery plus, if in For Plus it&#x27;s in my life, plus etcetera till a feminine so and within. With equal two point 09 102 for Section B, take the 1st and 2nd derivatives off FX because effort double dash X is decreasing on the interval, one to do. The maximum value occurs at the left. Interval pound 81 1. Yeah. This is the lower limit for King. So if slash x equal minus one over exist where the blind bite you is a power one over x the federal dash X equal toe over. Execute multiplied by It was a power one by not one over X plus one block plus three look dreary. Last one. So far X is about four multiplied. Boy e is about our one over X. By substitution, we find that if fallible dash at X equal to equal Oh, boy. 515 and the F at X equal one equal 8.154 And this is the value off K, Uschi A equal one and p equal to In the e t equations off. We will find 80 equal. Okay, but the blue eyed boy B minus a Yeah, que Well, what? Well, and Miss Squared my director institution. We&#x27;ll find that it is smaller than sorry. He teach smaller than particularly Bob Wind Oh, 68 And using Kale equal one and be equal to in the e m equations off. So he am smaller than or equal key about the blind boy. B minus e que Well, What During 34 in the square. 24. Any square so e m. Smaller than or equal or going for 34 four section C If X equals e to the power one over X so if finish x equal A to the power one over X off the blind boy minus X to the barber minus two. If global Dash X will equal he to the power one over X multiplied by two x plus one over experts of our four F global dish is decreasing and more than 04 so the maximum is at X equal. One key equal, incurable dish for X equal one equal three e about it going 15 for eight. But since then, the Bozidar by said that trapezoidal error bound expression to smaller than or equal over a who won. So we will find that K multiplied. B minus A. You will, sir 12 in the square, smaller than or equal or going toe one. So ST e the blood boy to minus one. Q. Over the wealth in this world smaller than or equal who went Oh, go on. So e over four in the square. Smaller than what we&#x27;re going toe one and so and with bigger them for equal. No. You for what went for for 44 About 82 wait for rounding up to the nearest integral. So in equal it is three bye said the midpoint. Error bound expression toe 2.1. So key applied by P minus Take you over 24 in the square. Well, smaller than equal. We&#x27;re goingto one by directive institution. We will find that in the square. Well, bigger than e over eight multiplied boy. Oh, fun. And then and then will bigger them or equal 58.3 and rounding up to the nearest integral. So in we&#x27;re equal 59.

Yuou Sun · Answer

Okay, I start. I want to find the t&#x27;s up. 10. I&#x27;m something. We know the function is this one and we know and is equal to 10 right? And the B and es We know everything. So just use this formula here he end. And over here, ama, with this formula, we can compute. He turned and just calculation, there&#x27;s no tricks here. Just calculate you have got to park out there. Here, R B, we need to have to make the arrest. Here&#x27;s a function here, here to function. So we want to know. Okay, were Kay&#x27;s. So we need to know the upper ball off the second directive. Right? Let&#x27;s start after is equal to eat to the one of our acts. Oh, sorry. Ah. Of prime is ego Thio, Uh, minus X square or one time? Speak to the and a prime prime is the go to X more Ah, maybe maybe in other ways. Quicker, right? Minus Thanks. There. Finest too. I need to the thus. Thanks times. Ah, minus X square times me to the ex. What? That&#x27;s because the directive, right? You prime We plus you re price right and is to e Thanks. Plus right. Plus, there&#x27;s a negative Negative, that&#x27;s for Yeah. I need to be right. We want to find the maxim off the front crime. So we take us our directive. We can off. Where&#x27;s needs me? That surgery is smaller than zero. Right? If we take a directive up this one and it becomes a negative what? Take a drag her off this once you become a negative, and this one is also connected. One so so certain Detective is smaller than Gerald. You cannot have next him. Hello. Oh, this is when that. But actually it&#x27;s equal to what? So the So the maximum is three. Right? When we know that K is equal to three, uh, use the formula K times once where a cube. They only bite Wow. Times 10 square. Where is he going? To written me more, right? And used a calculator. You can find that, uh, this is equal to 6.8 times. Tend to the captives free. They&#x27;re the three, right? And use a formula here. We can find a yam. It&#x27;s just 1/2 off the e t. My biggest fear is that 24 years, so yeah, it&#x27;s 3.4 times tend towards an active three. Here&#x27;s party Parsi. How long do we have to choose in such that they&#x27;re accurate to within? I wonder where that is. One weird 10,000 right? Yeah, It was a former gang three he derided by Wow, and Square is smaller than Yeah, Here&#x27;s the formula hand just technically. And there&#x27;s equal to the square here, then 83 and the 2nd 1 just. He raised his 12 and write a 44 here and just solved the potion equality. And they were heard of 59 that&#x27;s all.

Yuou Sun · Answer

Okay. Problem 21 first part A. We wantto speculate. T turn on turn asked. Her function is quite easy. Right. So we can just use Ah, one minute here. He, um and asked, you know, everything in the formula. Just use a formula hand calculate for the correct answer. After technically we can I he is he go to one point by a 35 a mystical to 2.0 eight to and ask is you go to to a point 00 You know what? Well, as it&#x27;s quite bad, I see the best right part b o and we should find the corresponding Aris. We have a form of that here. I just copied it from the book. Ut Yeah, have? Yes, right? So we want to know the K. Okay, it&#x27;s ah, second drag kid. Oh, since the function is quite easy, we can&#x27;t know that the second directive is also side axe. But there&#x27;s a man. It&#x27;s about there is a negative, but it doesn&#x27;t matter. So Kay is always equal to what? And the force directive off. If it&#x27;s just, I ax So the the maximum age also just what we can use this. Uh, okay. Times high. Okay, let&#x27;s start. The T is equal to one times higher to the three. Ready by it. Wow. Oh, was the end I forgot. And it&#x27;s a good 10 right? And yeah, it&#x27;s just Hi. No. Oh, this is 24. Sorry. 24 times. And yes, it&#x27;s just hi to defy and divided by what&#x27;s coming again. Oh, 180 times. 10 to the fourth, right. E We want to calculate the act. The extra iris right? We can just in to grow This function is to off its opener. Sweet, right? Yes, Cy, Thanks. Hero to pie. He acts these people toe cause I wa minus costs I minus one, right? Oh, hi. Sorry. Oh, cause I empire minus zero Oh, cause and zero minutes causing pie. Sorry when those coast line pie. So it&#x27;s just too right because all all our solutions is equal to two. Right? So we can compute actual Aras at Dr Iris. Let me see. Ah, yeah, Yeah, I minus he two minus one point night, eh? 35 It&#x27;s just through here. Oh, I say what right. No problem. And yeah, um, privacy. Go toe to toe minus 0.0 a two. My best deal. Two on us, equal to minus 0000 What? Right. Remember, huh? How long do we have to choose? And so that a proclamation effort? We&#x27;ve seen one nowhere. While 1234 Bye. You can make a father hi to the hell. Yeah, I divide five Times Square is more quit then. Oh, how many? 05 right? And just Yes, the solve it. And he&#x27;s quicker than I o a well nigh. Am I Correct? Yeah, I&#x27;m cracked, huh? And the 2nd £1 of served wine. Just use a formula here, and we have Ah, your question. Just solve the caution. We can get the answer right?

Yuou Sun · Answer

problem. 19 party is quite easy because it&#x27;s just calculation. We have the function to have the B A N is equal to eight. Right? And he&#x27;s able to eight so we can calculate t eight. And I am eight through this formula here and here. Right? Just calculate and you can&#x27;t get out, sir, On part B is to mate. Estimate the arrows. Okay, We have a formula here, Terrebonne. So we need to find the upper bone off the second director of back. Right. Let&#x27;s start access. You go to call sign, I swear. But so I prime is able to two acts times sign negative, Cy Axe. Where and second directive is to minus two times Cy. I&#x27;m square clothes. Thanks. Pains to axe times cause I X square. So the abs absolute off burial is this is smaller, then. Science axes. What are the one two acts since axes for the one and quicker than zero. So this is 22 times, two times one times. This is one of the one. It&#x27;s ah, six. Right here we get. The case is equal to six and we have this formula and you have the formula. Casey go six b A and they&#x27;re all knowing. So the e t you is what are then six times one right? Guided by 12 times Age square, there&#x27;s just one or 100. Okay, Yeah. You don&#x27;t have to calculate am again because you know that I am is just ah, half off you cheap. So it&#x27;s smaller, then 256 right? Okay, here&#x27;s Parsi. How long do we have to choose in? Oh, okay. Used formula. Hey, six times one already by its wow times and square is Mari Ko 10. Since I wasn&#x27;t right, um, to square it is greater than five. Sudden. Oh, there&#x27;s no to here And there&#x27;s quick witted and 71 because he&#x27;s a ***. Right on the second while is just two in the square is acquitted and 5000 seems there&#x27;s a two over here And that&#x27;s where is greater than to Southern 500 they&#x27;re squared And 50. Here&#x27;s Alyssa, right? Yeah,

Jiji Peter · Answer

answer for Question 17. Section eight. Using Travis Order Rule. If A and B is divided in tow, end some intervals each off lens Delta X within the points at explode X one x two still x m Zim tiene equal built the X over in the blade boy If it snowed plus toe if x one plus do if x ago lost two if x three Okay, toe if X in the minus two plus who if x in the minus one. Okay, must if it&#x27;s in So and for interpretation from 0 to 1. For design excess group the X and in equals 10. We will find the interval weights. Does the X equals B minus a over king equal one minus 0/8 or going 1 to 5. Then we calculate the values at the interval. Boundaries for FX equal cosigned X squared right at each X, we will get the value off design. Texas work at X equals zero one and we&#x27;re going 1 to 5 equal. We&#x27;re going nine 998 Yeah, at x equal or going toe five. This value equal ballpoint 998 and at X equal or going to 375 Jose Nexus were equal or going 990 etcetera. We will get this value. Add X equal. We&#x27;re going five and X equal for going 6 to 5, and we&#x27;re going to 75 and we&#x27;re going to 875 and finally at one. And, of course, at X equal one if x equal. 4.54 zero stream. What? And then we write out the proviso the rule for in the plus one terms and in our case, equal nine tons and fill in the on the field in the numbers of from the table. So t eight equal for going 1 to 5 over to amongst the blind boy, one plus to off the blue eyed boy Go going to 9998 plus two multiplied boy or going +998 Glass toe the blue eyed boy Oh boy. 990 plus two multiplied boy for going tonight 68 no. 1.968 and etcetera, still 4.54 zero street and the result off T a equal Oh boy, 90 toe 33 and using his midbrain tool. If A and B is divided in tow. End some intervals each off lens, Delta, X and M Boy is the midpoint off Oy, some interval. Then I am in equal some mission from all equal one toe end for if off in my just days. Then it calculates the values at the midpoint off each interval at X, we will give the value off FX. We will get the F X values at X equal 4.6 That takes a boy at X equal going toe 18 at X equal over in 31 Ethics equal or going for three at X equals 4.56 and X equal. We&#x27;re going 68 and X equal. We&#x27;re going to 81 x equal or 0.93 By separating these values, we will find that if it&#x27;s equal here, we&#x27;re going to 999 and here 4.9 993 and it&#x27;s equal or going for three. If it&#x27;s equal for going to nine 81 seven for one 95 we&#x27;re going to 89 178 and at X equal over in 93 x equal. Oh boy six ST. And for the midpoint tool We multiply the bits off each interval Delta X times So some off each fx from the midpoint tables So we find that they made equal these things multiplied, boy, If in one plus if we do plus if industry yes, if they before plus if invite Plus if m six plus if in seven plus if in eight the direct substitution, we will find that inmate equal or going to 905 62 95 six for section B Piece of booze Just yeah, four X Okay. And mean if 80 and ian our errors in the trapezoidal and the midpoint through then 80 equal. Sorry. Smaller than or equal key PM I must say it is about you over wealth in the square and Okay, um, and eaten equal. Sorry. Smaller than or equal. Okay, Mr Bligh. Boy, P minus E que Overall 24 in the square who affects equals X squared. Using differentiate, we will find that if financial X equal minus two x Zain exist word and again differentiate the double dash X equal minus two. Zain X squared minus four X squared. Who? Zion. Exit squares. All right, so if you double dash X equal to Zion exist square plus four access world multiplied boy design exist word this is more than or equal two plus four equal six therefore k equal six substitute being equal one. It was zero in equal. It indicate equal six. So eating smaller than or equal six multiplied by one minus zero over when multiplied boy 80 square this equal Wow. Over equal or going for for 78 1 to 5. Yeah, and the M mhm. Yeah, equal six. That applied by one minus zero was about you over 24 of the blind by eight square by direct substitution. Equally or when? Well, well, three Mine 06 Yes, for preaching 17 Section C and record from Barkevious E equals zero. Me equal one okay, Equals six. So et smaller then or equal with who or one Sure. Six over 12 in this word. Smaller than or equal or went or or one so six smaller than or equal. We&#x27;re going to go go 12 in the square. So what? What I was saying in so right 71 Smaller than or equal in. And I am also smaller than or equal or going toe one. So this value smaller than or equal six over 24 in the square, smaller than or equal or going to a one. So 60 smaller than or equal for win 4424 in the square. So, yeah, so 50 is equal than or smaller than or equal in.

Michael Twiton · Answer

the finger gives us that K two is going to develop by one. Then the area trump. Is it a rule we&#x27;re using? Tense of intervals is bounded above by a one times the length of the interval cube, divided by 12 times and squared and being 10. So it&#x27;s 27 devoted by 12 times 100. We may cancel a factor of three to get nine over 400. No, the Arab owned using the midpoint rule is just 1/2 of fat. So it&#x27;s gonna be nine over 800. And generally speaking, the midpoint rule using and some intervals has there one times 27 over 24 times and squared. And we would like this to be it most one million&#x27;s. If you re arrange this, we get and squared has to be a larger equal to 27 million over 24 and that gives and has to be larger or equal to 1000 and 61 so you can use this particular number 1061 for in

Problem

(a) Find the approximations $T_{10}, M_{10},$ and…

Problem 18 Medium Difficulty

Answer

a) $$
2.0191
$$
b) $$
\approx 0.0034
$$
c) $$
n=59
$$

Related Courses

Essential Calculus Early Transcendentals

Related Topics

Discussion

Top Calculus 2 / BC Educators

Catherine R.

Heather Z.

Kayleah T.

Caleb E.

Calculus 2 / BC Courses

Integration Review - Intro

Definite vs Indefinite

Recommended Videos

Watch More Solved Questions in Chapter 6

Video Transcript

James Stewart

Essential Calculus Early Transcendentals

Catherine R.

Heather Z.

Kayleah T.

Caleb E.

Integration Review - Intro

Definite vs Indefinite

What do you need help with?

Textbooks

Ask a question

Courses

AI Tutor

a) $$2.0191 $$b) $$\approx 0.0034$$c) $$n=59$$

Essential Calculus Early Transcendentals

Catherine R.

Heather Z.

Kayleah T.

Caleb E.

Integration Review - Intro

Definite vs Indefinite

James StewartEssential Calculus Early Transcendentals

Catherine R.

Heather Z.

Kayleah T.

Caleb E.

a) $$
2.0191
$$
b) $$
\approx 0.0034
$$
c) $$
n=59
$$

James Stewart

Essential Calculus Early Transcendentals