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Chapter 8: Q 5. (page 703)

Give precise mathematical definitions or descriptions of the concept that follows. Then illustrate the definition or description with a graph or an algebraic example.

Maclaurin polynomial

Short Answer

Expert verified

A Maclaurin Polynomial is a subset of the Taylor Polynomial in which zero serves as the sole point.

Step by step solution

01

Step 1. Given information

The concept is "Maclaurin polynomial".

02

Step 2. Explanation

The Taylor Series, also known as the Taylor Polynomial, is a representation of a function as an infinite sum of terms determined from its derivative values at a single point. A Maclaurin Polynomial is a subset of the Taylor Polynomial in which zero serves as the sole point.

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Most popular questions from this chapter

The second-order differential equation

x2y''+xy'+x2-p2=0

where p is a nonnegative integer, arises in many applications in physics and engineering, including one model for the vibration of a beaten drum. The solution of the differential equation is called the Bessel function of order p, denoted by Jp(x). It may be shown that Jp(x) is given by the following power series in x:

Jp(x)=∑k=0∞(-1)kk!(k+p)!22k+px2k+p

Find and graph the first four terms in the sequence of partial sums of Jo(x).

Use an appropriate Maclaurin series to find the values of the series in Exercises 17–22.

∑k=0∞-1πk

What is x0if the interval of convergence for the power series ∑k=0∞ akx−x0kis(2,10]?

What is the relationship between a Maclaurin series and a power series in x?

Show that ∑k=0∞ 11+2kxk, the power series in xfrom Example 1, diverges when x=-2
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