Real analysis | Inequalities | Symmetric functions

Maclaurin's inequality

In mathematics, Maclaurin's inequality, named after Colin Maclaurin, is a refinement of the inequality of arithmetic and geometric means. Let a1, a2, ..., an be positive real numbers, and for k = 1, 2, ..., n define the averages Sk as follows: The numerator of this fraction is the elementary symmetric polynomial of degree k in the n variables a1, a2, ..., an, that is, the sum of all products of k of the numbers a1, a2, ..., an with the indices in increasing order. The denominator is the number of terms in the numerator, the binomial coefficient Maclaurin's inequality is the following chain of inequalities: with equality if and only if all the ai are equal. For n = 2, this gives the usual inequality of arithmetic and geometric means of two numbers. Maclaurin's inequality is well illustrated by the case n = 4: Maclaurin's inequality can be proved using Newton's inequalities. (Wikipedia).

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Determine the Maclaurin Series and Polynomial for Function in the Form ax^2*e^(bx)

This video explains how to determine a Maclaurin series and Maclaurin polynomial for a a function using a known power series and a product. The results are verified graphically. Site: http://mathispower4u.com

From playlist Power Series

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How to Compute a Maclaurin Polynomial

Free ebook http://bookboon.com/en/learn-calculus-2-on-your-mobile-device-ebook What is a Maclaurin polynomial? In mathematics, a Taylor series is a representation of a function as an infinite sum of terms that are calculated from the values of the function's derivatives at a single point

From playlist A second course in university calculus.

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Calculus 2: Infinite Sequences and Series (81 of 86) The Taylor Series Revisisted

Visit http://ilectureonline.com for more math and science lectures! In this video I will explain further what is the Taylor series, what it does for us, and how is it different from the Maclaurin series. Next video in the series can be seen at: https://youtu.be/iXwy9N6x8AQ

From playlist CALCULUS 2 CH 14 SERIES AND SEQUENCES

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Calculus 2: Infinite Sequences and Series (63 of 86) What is the Maclaurin Series?

Visit http://ilectureonline.com for more math and science lectures! In this video I will show how the Maclaurin series is derived form the Taylor series. Next video in the series can be seen at: https://youtu.be/HRCGwOm36-Q

From playlist CALCULUS 2 CH 14 SERIES AND SEQUENCES

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Introduction to Taylor and Maclaurin Polynomials

Introduction to Taylor and Maclaurin Polynomials If you enjoyed this video please consider liking, sharing, and subscribing. You can also help support my channel by becoming a member https://www.youtube.com/channel/UCr7lmzIk63PZnBw3bezl-Mg/join Thank you:)

From playlist Larson Calculus 9.7 Taylor Polynomials and Approximations

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Taylor's inequality (KristaKingMath)

► My Sequences & Series course: https://www.kristakingmath.com/sequences-and-series-course Learn how to use Taylor's inequality to show that the sum of a Maclaurin series is representative of the series for all values of x. ● ● ● GET EXTRA HELP ● ● ● If you could use some extra help wit

From playlist Sequences & Series

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Math 2B. Calculus. Lecture 27. Taylor Series and Maclaurin Series

UCI Math 2B: Single-Variable Calculus (Fall 2013) Lec 27. Single-Variable Calculus -- Taylor Series and Maclaurin Series -- View the complete course: http://ocw.uci.edu/courses/math_2b_calculus.html Instructor: Natalia L. Komarova Ph.D. License: Creative Commons CC-BY-SA Terms of Use: htt

From playlist Math 2B: Calculus

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Determine the Maclaurin Series and Polynomial for Function in the Form a*cos(bx^2)

This video explains how to determine a Maclaurin series and Maclaurin polynomial for a a function using a known power series and a product. The results are verified graphically. Site: http://mathispower4u.com

From playlist Power Series

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Taylor and Maclaurin Series

This video explains how to determine a Taylor and Maclaurin series to represent a function. http://mathispower4u.yolasite.com/

From playlist Power Series

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Maclaurin series and applications

Free ebook http://bookboon.com/en/learn-calculus-2-on-your-mobile-device-ebook Basic example on Maclaurin series and some applications. In mathematics, a Taylor series is a representation of a function as an infinite sum of terms that are calculated from the values of the function's deriv

From playlist A second course in university calculus.

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Real Analysis | Pointwise convergence of sequences of functions.

We introduce the notion of a sequence of functions, give the definition of pointwise convergence, and look at three examples. Please Subscribe: https://www.youtube.com/michaelpennmath?sub_confirmation=1 Merch: https://teespring.com/stores/michael-penn-math Personal Website: http://www.mi

From playlist Real Analysis

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Ex: Find a Degree One and Degree Two Maclaurin Polynomial

This video explains how to determine a Maclaurin polynomial for a basic exponential function. the results are verified graphically. Site: http://mathispower4u.com

From playlist Power Series

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Calculus 11.10 Taylor and Maclaurin Series

My notes are available at http://asherbroberts.com/ (so you can write along with me). Calculus: Early Transcendentals 8th Edition by James Stewart

From playlist Calculus

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Taylor's Inequality

Thanks to all of you who support me on Patreon. You da real mvps! $1 per month helps!! :) https://www.patreon.com/patrickjmt !! Taylor's Inequality - Examples are shown using Taylor's Inequality. In the first part, I show that a series expansion is valid using Taylor's Inequality. In

From playlist Calculus / Second Semester - Integration

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Futher Pure 2 FP2 Maclaurin Series 7 Exam Style Questions 1 Past paper Edexcel

www.m4ths.com GCSE and A Level Worksheets, videos and helpbooks. Full course help for Foundation and Higher GCSE 9-1 Maths All content created by Steve Blades

From playlist Futher Pure 2 FP2 Maclaurin and Taylor Series

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Calculus BC - Unit 5 Lesson 2: Lagrange Error Bound

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From playlist AP Calculus BC

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Multivariable Taylor Polynomials

Free ebook http://tinyurl.com/EngMathYT A lecture on how to calculate Taylor polynomials and series for functions of two variables. Such ideas are useful in approximation of functions. We show where the polynomial representation comes from.

From playlist Mathematics for Finance & Actuarial Studies 2

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Gronwall's inequality & fractional differential equations

Several general versions of Gronwall's inequality are presented and applied to fractional differential equations of arbitrary order. Applications include: yielding a priori bounds and nonumultiplicity of solutions. This presentation features new mathematical research. http://projecteucli

From playlist Mathematical analysis and applications

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The Maclaurin Series for f(x) = e^x

Calculus: We derive the Maclaurin series for e^x and estimate e^{-1} by way of the error estimate for alternating series. For more videos like this one, please visit the Calculus playlists at this channel.

From playlist Calculus Pt 6: Sequences and Series

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Futher Pure 2 FP2 Maclaurin Series 4 Differentiation and Standard Results

www.m4ths.com GCSE and A Level Worksheets, videos and helpbooks. Full course help for Foundation and Higher GCSE 9-1 Maths All content created by Steve Blades

From playlist Futher Pure 2 FP2 Maclaurin and Taylor Series

Related pages

Elementary symmetric polynomial | Inequality of arithmetic and geometric means | If and only if | Binomial coefficient | Mathematics | Inequality (mathematics) | Real number | Newton's inequalities | Muirhead's inequality