Differentials To Approximate The Maximum Possible Error
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Use Differentials To Approximate The Maximum Error
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Differentials To Approximate Square Root
Integers Ordering and Comparing Integers Adding Integers Adding Integers on a Number Line Subtracting Integers Subtracting Integers on a Number Line Multiplying Integers Dividing Integers Exponents and Integers differentials to approximate volume Factors and Multiples > Divisibility of Integers Even Numbers (Integers) Odd Numbers (Integers) Divisibility Rules What are Factors and Multiples Integer Factorization What is a Prime Number Composite Numbers How do you do Prime Factorization Greatest Common Divisor (GCD) Least Common Multiple (LCM) Fractions > What is Fraction Proper Fractions Improper Fractions Mixed Numbers/Fractions Mixed differentials to approximate cube root Numbers on a Number Line Equivalent Fractions Reducing Fractions Adding Fractions with Like Denominators Subtracting Fractions with Like Denominators Adding Fractions with Unlike Denominators Subtracting Fractions with Unlike Denominators Converting Mixed Numbers to Improper Fractions Converting Improper Fractions to Mixed Numbers Adding Fractions with Whole Numbers Subtracting Fractions with Whole Numbers Adding Mixed Numbers Subtracting Mixed Numbers Comparing Fractions Multiplying Fractions Multiplying Mixed Numbers Dividing Fractions by Whole Number Dividing Fractions Dividing Mixed Numbers Reciprocals Negative Exponents Rational Numbers Decimals > What is Decimal Decimals Place Value Rounding Decimals Decimal Number Line Comparing Decimals Powers of 10 Scientific Notation Decimal Fractions Converting Decimals To Fractions Converting Fractions to Decimals Adding Decimals Subtracting Decimals Multiplying Decimals Dividing Decimals by Whole Numbers Dividing Whole Numbers by Decimals Dividing Decimals Repeating (Recurring) Decimals Absolute Value Percents > What is Percent Converting Decimals to Percents Converting Percents to Decimals Irrational Numbers > Squares and Square Roots Perfect Square Cubes and Cube Roots Perfect Cube Nth Root What is Irrational
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Use Differentials To Approximate The Value Of The Expression
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Use Differentials To Estimate The Maximum Error In The Calculated Volume.
niet beschikbaar. WeergavewachtrijWachtrijWeergavewachtrijWachtrij Alles verwijderenOntkoppelen Laden... Weergavewachtrij Wachtrij __count__/__total__ Errors Approximations Using Differentials IMA Videos AbonnerenGeabonneerdAfmelden33.01733K Laden... Laden... Bezig... Toevoegen aan Wil je hier later nog een keer naar kijken? Log in om deze video toe http://www.emathhelp.net/notes/calculus-1/differentials/using-differentials-to-estimate-errors/ te voegen aan een afspeellijst. Inloggen Delen Meer Rapporteren Wil je een melding indienen over de video? Log in om ongepaste content te melden. Inloggen Transcript Statistieken 17.226 weergaven 27 Vind je dit een leuke video? Log in om je mening te geven. Inloggen 28 15 Vind je dit geen leuke video? Log in om je mening te geven. Inloggen 16 Laden... Laden... Transcript Het interactieve transcript kan niet worden geladen. https://www.youtube.com/watch?v=kXkwrhdqXWg Laden... Laden... Beoordelingen zijn beschikbaar wanneer de video is verhuurd. Deze functie is momenteel niet beschikbaar. Probeer het later opnieuw. Gepubliceerd op 4 aug. 2012Errors & Approximation - Application of Derivative ( Use of Differentials) - There are many application of derivative concept in calculus mathematics. One of them is Errors and Approximation. We can easily solve question related to errors in physics as well as mathematics using the concept of derivative , using the concept of differentials.In this Calculus video, we use differential's concept to find the approximate error in calculating the volume of a sphere. For this we know the radius of the sphere and we know the error while calculating the radius of that sphere. Now we have to use the concept of differentials to find the approximate errors while calculating the entire volume the sphere.This video calculus video is created under the application of derivative ( use of differentials) playlist . For complete list of videos on use of differentials click the link below- http://www.youtube.com/playlist?list=...To play the Application of Derivative from beginning click here - http://www.youtube.com/watch?v=CGQ6sa... I hope this calculus video will help you to enhance the concept of use of differentials -application of Derivative Categorie Onderwijs Licentie Standaard YouTube-licentie Meer weergeven Minder weergeven Laden... Advertentie Autoplay Wanneer a
Lesson 2.9. It would be healthy to go back and briefly review our first contact with this topic. In the two graphs above, we are reminded of the principle that a tangent line to a curve at a certain point can be a good approximation of the value of http://www.blc.edu/fac/rbuelow/calc/nt3-8.html a function if we are "close by" the point we are interested in. In the above graphs, we see that near the point (8,2) (the point of tangency) the green tangent is extremely close to the red original curve. We also notice that the closer we get to the point of tangency, the more accurate our linear approximation is. If you have the Journey Through Calculus CD, load and run MResources/Module 3/Linear Approximations/Start of Linear Approximations. Example problem: Find differentials to a linear approximation or linearization for . Use this approximation to estimate . We first calculate the derivative of the function. This will allow us to know the general formula for the slope of the tangent line at any point on the curve. Next, we need to find the slope of the tangent line at x = 5. Now we can begin to formulate the equation of the tangent line, because we know its specific slope. We now subsitute in differentials to approximate the coordinates of the given point or (5,1.71) and solve for b. We now have our linear approximation. Now we can find our estimate for the cube root of 5.03 Differentials If we take the two derivative notations that we have been using and set them equal, we have the equation: . If we then multiply both sides of this equation by we get: . This equation shows that we can calculate dy as a dependent variable, based on the inputs of dependent variables x and dx.This means that we can calculate an estimated error (dy) in linear approximation using such a formula. An example follows. Sample Problem: The radius of a sphere was measured and found to be 21 cm with a possible error in measurement of at most 0.05 cm. What is the maximum error in using this value of the radius to compute the volume of the sphere? If the radius of the sphere is r then its volume is . If the error in the measured value of r is denoted by then the corresponding error in the calculated value of V is , which can be approximated by the differential . When r = 21 and dr = 0.05, this becomes: Therefore, the maximum error in the calculated volume is about 277 cubic centimeters. Links to Other Explanations of Differentials: Differentials Mathematics Help Central University of Kentucky Tutorial on Differentials If