Differentials To Estimate The Maximum Error
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Use Differentials To Estimate The Maximum Error In The Calculated Surface Area
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Use Differentials To Estimate The Propagated Error
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Use A Linear Approximation Or Differentials To Estimate The Given Number 1.999 4
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Use Differentials To Estimate The Amount Of Metal In A Closed Cylindrical Can
hieronder wijzigen. Learn more You're viewing YouTube in Dutch. You can change this preference below. Sluiten Ja, nieuwe versie behouden Ongedaan maken Sluiten Deze video is http://www.emathhelp.net/notes/calculus-1/differentials/using-differentials-to-estimate-errors/ niet beschikbaar. WeergavewachtrijWachtrijWeergavewachtrijWachtrij Alles verwijderenOntkoppelen Laden... Weergavewachtrij Wachtrij __count__/__total__ Using differentials to estimate maximum error Mitch Keller AbonnerenGeabonneerdAfmelden3636 Laden... Laden... Bezig... Toevoegen aan Wil je hier later nog een keer naar kijken? Log in om deze video toe te voegen aan een afspeellijst. Inloggen Delen Meer Rapporteren Wil je een melding indienen over de https://www.youtube.com/watch?v=pFtpxooa7kw video? Log in om ongepaste content te melden. Inloggen Transcript Statistieken 5.950 weergaven 6 Vind je dit een leuke video? Log in om je mening te geven. Inloggen 7 2 Vind je dit geen leuke video? Log in om je mening te geven. Inloggen 3 Laden... Laden... Transcript Het interactieve transcript kan niet worden geladen. Laden... Laden... Beoordelingen zijn beschikbaar wanneer de video is verhuurd. Deze functie is momenteel niet beschikbaar. Probeer het later opnieuw. Gepubliceerd op 6 feb. 2014An example of using differentials to determine the maximum error in a volume calculation if you know the manufacturing error possibilities for the dimensions Categorie Onderwijs Licentie Standaard YouTube-licentie Meer weergeven Minder weergeven Laden... Autoplay Wanneer autoplay is ingeschakeld, wordt een aanbevolen video automatisch als volgende afgespeeld. Volgende Errors Approximations Using Differentials - Duur: 5:24. IMA Videos 17.127 weergaven 5:24 Calculus - Differentials with Relative and Percent Error - Duur: 8:34. Stacie Sayles 3.364 weergaven 8:34 Greatest Possible Error - Duur
here for a quick overview of the site Help Center Detailed answers to any questions you might have Meta Discuss the workings and policies of this site About Us Learn more about Stack Overflow the company Business Learn more about hiring developers or posting http://math.stackexchange.com/questions/1066568/use-differentials-to-estimate-the-error-in-volume-of-the-box ads with us Mathematics Questions Tags Users Badges Unanswered Ask Question _ Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute: Sign up Here's how it works: Anybody can ask a question Anybody can answer The best answers are voted up and rise to the top Use differentials to estimate the error in volume of the box. up vote 0 down vote differentials to favorite In a manufacturing process the boxes with nominal dimensions of $5$ inches by $5$ inches by $2$ inches are subject to an error of $1\%$ in each dimension.Use differentials to estimate the error in volume of the box. Compare it with the actual minimum and maximum value of the box. I do not know how we can solve such a problem. I am completely lost. Please help me. calculus volume share|cite|improve this question edited Dec 13 '14 at 19:40 enzotib differentials to estimate 4,77221026 asked Dec 13 '14 at 18:08 user163993 257112 the volume is $5\times 5\times \times 2=50$ –user163993 Dec 13 '14 at 18:15 Can I use this? if we take $x=5,y=5,z=2$ then $V=xyz$ this implies $dv=yzdx+xzdy+xydz=0.1+0.1+0.25=0.45$ –user163993 Dec 13 '14 at 18:19 so error in volume is $45\%$,Is this correct? –user163993 Dec 13 '14 at 18:20 And what should I do about the the second part?Its comparison with maximum and minimum value of the box?I do not know the maximum and minimum value of the box. –user163993 Dec 13 '14 at 18:21 $dv$ has units of volume. $dv/v = 0.9 \%$. –Jas Ter Dec 13 '14 at 19:05 | show 2 more comments 1 Answer 1 active oldest votes up vote 1 down vote accepted The volume of a box with dimensions $a$, $b$, $c$ is given by $$V(a,b,c)=a\>b\>c\ .$$ It follows that $${dV(a,b,c)\over V(a,b,c)}={da\over a}+{db\over b}+{dc\over c}\ .$$ Therefore, "in first approximation", the relative error in volume is the sum of the relative errors in the side lengths. In the given example the relative errors in the side lengths are $1\%$. As the case may be these add up, and we obtain a relative volume error of $3\%$, or $1.5$ cubic inches as a "first estimate". The actual minimal volume of the box under the given constraints is $$4.95\cdot 4.95\cdot1.98=48.51495$$ cubic inches, which is $<1.5$ cubic inches off; and the maxim