Taylor polynomial approximation

Related BrainMass Solutions

• Taylor Polynomial

  BrainMass Posting Solution# MATH 7739 Basics: A Taylor Polynomial is an approximation of an elementary function f(x) centered at a particular value of x, say at x = c.

• Taylor polynomials

  As you can see, the Taylor polynomial is only good for the first few degrees on the horizontal axis. The approximation can be improved by having more terms on the right hand side of the equation.

• 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

• Quadratic Taylor Polynomial

  137128 Quadratic Taylor Polynomial Problem Suppose that p(x) = 3 - 4x + x² is the quadratic Taylor polynomial approximation based at Xο (ο is a subscript for x) = 1 to a function g.

• Taylor Series, Radius of Convergence

  (d) Use Taylor polynomial of degree 5 to give an approximation to ln?(2). (e) Use the error term from Taylor's Theorem to show that the error in (d) is at most 1/6. (Note that this is still not a particularly good approximation.)

• 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.

• General Calculus Questions : Definition of a Limit and Derivative, Product Rule, Tangent Line Approximation, Taylor Polynomial, Newton's Method, L'Hopital's Rule, MVT, IVT, Fundamental Theorem

  What is the tangent line approximation to a function? 5. What is the Taylor polynomial approximation to a function?

• Differential Equation Application

  Sketch the field and use it to determine whether the estimate is an overestimate or an underestimate. 3) Find the Taylor polynomial of degree 4 as an approximation of the Solution of the initial problem.

• 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.