Purchase Solution

Approximation of Integrals and Taylor Polynomials

Not what you're looking for?

Ask Custom Question

Given ( INTEGRAL ln square(x)dx, as x from n to n+1 ) = ( INTEGRAL ln square (n+x)dx, as x from 0 to 1 ) = ( INTEGRAL [[ln(n+x) - ln(x) + ln(n)]square] dx, as x from 0 to 1 ),

(a) Verify that ( LIMIT (n/ln(n)) [INTEGRAL (ln square (x)dx) - (ln square (n))] as n approach to the infinity ) = 1

(b) Compute LIMIT ((n square)/ln(n)) [ INTEGRAL ln square (x)dx - ln square (n) - ((ln(n))/n)]

Purchase this Solution
Solution Summary

Taylor polynomials are used to define limits are given. The approximation of integrals and taylor polynomials are analyzed.

Solution Preview

Please see the attached file for the full solution.

Thanks for using BrainMass.

Well, before starting to solve the problem, I should mention that there is some vagueness in the question. From the description of the problem, I have figured out that I would use Taylor polynomials to approximate the integral. We have this information:

That I agree and there is no problem, but if you trust me, I will tell you that the following equation does not hold at all:

Upon your request, I can show you why, but for the moment let's forget about it. Of course, it is likely that there has been a typo.

Ok, it is possible, but time consuming to ...

Purchase this Solution
Free BrainMass Quizzes
Geometry - Real Life Application Problems

Understanding of how geometry applies to in real-world contexts

Graphs and Functions

This quiz helps you easily identify a function and test your understanding of ranges, domains , function inverses and transformations.

Know Your Linear Equations

Each question is a choice-summary multiple choice question that will present you with a linear equation and then make 4 statements about that equation. You must determine which of the 4 statements are true (if any) in regards to the equation.

Exponential Expressions

In this quiz, you will have a chance to practice basic terminology of exponential expressions and how to evaluate them.

Probability Quiz

Some questions on probability

View More Free Quizzes
Related BrainMass Solutions

  • Convergent or divergent series

    Write down the first 4 Taylor polynomials around zero and plot f(x) a long with its approximation Solution: Taylor Series for f(x) about x=0 Taylor polynomial of degree 0 is f(x) = f(0) f(x) = 2e Taylor polynomial of degree 1 is

  • Pade (Rational Function) Approximation

    Pade or rational functions are similar to approximations by Taylor polynomials. The method of finding a rational function from a given Taylor polynomial is described and several examples are worked in detail.

  • Taylor Polynomial

    =1*2*3=6) Taylor polynomials are discussed. The solution is detailed and well presented.

  • Quadratic Taylor Polynomial

    Quadratic Taylor Polynomials are investigated.

  • Taylor polynomials

    137122 Problems with Taylor polynomials First, find the Taylor polynomial Pn (n is a subscript) of order n for the function f with base point Xο (ο is a subscript). Then plot both f and Pn on the same axes.

  • Taylor Polynomials,Planck's Law and Rayleigh-Jeans Law

    When lambda is large this fraction is small and thus close to zero - so the approximation using the Taylor polynomial applies.

  • Taylor Approximation Related Problem

    10994 Taylor Approximation Related Problem Please see the attached file for the fully formatted problems. Questions pertain to Second order Taylor approximations and integrals for two first order differential equations.

  • Approximation with Taylor polynomials

    10700 Approximation with Taylor Polynomials: Example Problems Note:% just a symbol Let I be an open interval containing the point x.(x not), and suppose that the function f:I->R has a continuous third derivative with f'''(x)>0 for all x in I.

  • Numerical integration using Simpson and Gaussian quadrature

    We have a product ABC, where A and B are exactly calculated and C=D+E, where D is an approximation and E is the error. Then ABC=ABD+ABE. We recognize ABD as the approximation of the product ABC, and ABE as the error.

View More Related Solutions