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Chapter 8: Q. 38 (page 692)

In Exercises 41鈥�48 in Section 8.2, you were asked to find the fourth Taylor polynomial P4(x)for the specified function and the given value of x 0. Here give Lagrange鈥檚 form for the remainder role="math" localid="1650647764004" R4(x).

ex,1

Short Answer

Expert verified

Ans: R4(x)=ec120(x鈭�1)5

Step by step solution

01

Step 1. Given information.

given,

ex,1

02

Step 2. Consider the given function,

The Lagrange's form for the remainder is Rn(x)=f(n+1)(c)(n+1)!x鈭�x0n+1, where c is betweenx0andx.

Since f(x)=ex, so we have f(n+1)(c)=ecfor everyn鈮�0

Also, the series of Taylor, so use x0=1

Therefore,

Since f(5)(x)=exandx0=1then

role="math" localid="1650649900503" R4(x)=f5(c)5!(x鈭�1)5

That is,

role="math" localid="1650649942321" R4(x)=ec120(x鈭�1)5

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Most popular questions from this chapter

What is a power series in x-x0?

Find the interval of convergence for each power series in Exercises 21鈥�48. If the interval of convergence is finite, be sure to analyze the convergence at the endpoints.

鈭�k=0鈭�k!xk

Find the interval of convergence for power series: 鈭�k=1鈭�1k(x+2)k

Find the interval of convergence for power series:鈭�k=0鈭�k+13k2x-5k

In Exercises 41鈥�48 find the fourth Taylor polynomial P4(x)for the specified function and the given value of x0.

48.sin3x,蟺6
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