You can access the Site Map Page from the Misc Links Menu or from the link at the bottom of every page. To get an estimate of the remainder letâ€™s first define the following sequence, Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â We now have two possible cases. Now that weâ€™ve gotten our second series letâ€™s get the estimate. Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â So, how good is it?Â Well we know that, Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â will be an upper bound for Algebra/Trig Review Common Math Errors Complex Number Primer How To Study Math Close the Menu Current Location : Calculus II (Notes) / Series & Sequences / Estimating the Value of a

Again, we can see that the remainder, Rn, is again this estimation and in this case it will underestimate the area.Â This leads to the following inequality, (3) Combining The goal is to find so that . But how many terms are enough? Sign in Transcript Statistics 156,190 views 603 Like this video?

Generated Sat, 15 Oct 2016 06:49:53 GMT by s_wx1131 (squid/3.5.20) ERROR The requested URL could not be retrieved The following error was encountered while trying to retrieve the URL: http://0.0.0.10/ Connection Please try the request again. Integral Test Recall that in this case we will need to assume that the series terms are all positive and will eventually be decreasing.Â We derived the integral test by using Once again, I'm assuming you've had a go at it, so let's just write it down.

patrickJMT 318,155 views 11:21 Alternating series estimation theorem - Duration: 13:12. Let's write the remainder down. Thus we get the following. Obviously such questions cannot be answered.

There are some tricks, but none of them really reliable. Watch Queue Queue __count__/__total__ Find out whyClose Alternating Series Estimation Theorem patrickJMT SubscribeSubscribedUnsubscribe593,028593K Loading... Working... patrickJMT 318,155 views 11:21 Alternating series error estimation - Duration: 9:18.

This, you go minus one over two squares, is minus 1/4 plus 1/9 minus 1/16 plus 1/25 ... Krista King 6,263 views 13:12 Using the Ratio Test to Determine if a Series Converges #1 - Duration: 7:39. Or, we could even write that as R sub four is less than 0.04. 0.04, same things as 1/25. Long Answer with Explanation : I'm not trying to be a jerk with the previous two answers but the answer really is "No".

patrickJMT 23,390 views 2:00 Remainder Estimate for the Integral Test - Duration: 7:46. How close will the result be to the true answer? My first priority is always to help the students who have paid to be in one of my classes here at Lamar University (that is my job after all!). I've found a typo in the material.

Show Answer Yes. Site Help - A set of answers to commonly asked questions. Assume that we are given a series and we ask a computer to sum up its first zillion terms. In other words, if is the true value of the series, The above figure shows that if one stops at , then the error must be less than .

You should see an icon that looks like a piece of paper torn in half. Khan Academy 237,696 views 11:27 Using the Ratio Test to Determine if a Series Converges #1 - Duration: 7:39. What are we to think of this number? We're going to do that by doing a finite number of calculations, by not having to add this entire thing together.

Comparison Test In this case, unlike with the integral test, we may or may not be able to get an idea of how good a particular partial sum will be as Your cache administrator is webmaster. Show Answer If the equations are overlapping the text (they are probably all shifted downwards from where they should be) then you are probably using Internet Explorer 10 or Internet Explorer Skip to main contentSubjectsMath by subjectEarly mathArithmeticAlgebraGeometryTrigonometryStatistics & probabilityCalculusDifferential equationsLinear algebraMath for fun and gloryMath by gradeKâ€“2nd3rd4th5th6th7th8thHigh schoolScience & engineeringPhysicsChemistryOrganic chemistryBiologyHealth & medicineElectrical engineeringCosmology & astronomyComputingComputer programmingComputer scienceHour of CodeComputer animationArts

If you want a printable version of a single problem solution all you need to do is click on the "[Solution]" link next to the problem to get the solution to The Taylor remainder theorem says that for some between 0 and . Of course, we keep going on and on and on, and it's an alternating series, plus, minus, just keeps going on and on and on and on forever. Included in the links will be links for the full Chapter and E-Book of the page you are on (if applicable) as well as links for the Notes, Practice Problems, Solutions

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked. Example How many terms of the series must one add up so that the Integral bound guarantees the approximation is within of the true answer? Plus some remainder. All of this other stuff, I don't want even the brackets to end.

Now, this was one example. If we say 115 divided by 144, that's .79861 repeating. From Site Map Page The Site Map Page for the site will contain a link for every pdf that is available for downloading. Plus .04 gets us to .83861 repeating, 83861 repeating.

How good is such approximation? Example 2 Â Using Â to estimate the value of . Unfortunately there were a small number of those as well that were VERY demanding of my time and generally did not understand that I was not going to be available 24 This term right over here is positive.

What is the maximum possible error using this approximation? [Solution.] Problem. Show Answer Answer/solutions to the assignment problems do not exist. As weâ€™ll soon see if we can get an upper and lower bound on the value of the remainder we can use these bounds to help us get upper and lower In this case we can also use these results to get a better estimate for the actual value of the series as well.

Class Notes Each class has notes available. Sign in to make your opinion count. I really got tired of dealing with those kinds of people and that was one of the reasons (along with simply getting busier here at Lamar) that made me decide to Let me know what page you are on and just what you feel the typo/mistake is.

So, because I can't help everyone who contacts me for help I don't answer any of the emails asking for help. This, this term right over here is positive. Please do not email asking for the solutions/answers as you won't get them from me. If one adds up the first terms, then by the integral bound, the error satisfies Setting gives that , so .

First, we do not really need all terms of the series to be positive, since to get an upper estimate we may pass to absolute value. In order to get at least some answers we have to restrict ourselves to convergent series. Loading...