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Home Infinite Series Taylor's Formula Examples Example 1: Find Taylor Polynomials
 
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Example 1: Find Taylor Polynomials

Find the first five Taylor polynomials of sin x at x = 0. We work them out in Table 9.10.1.

Table 9.10.1

k

f(k)(x)

f(k)(0)

pk(x)

0

sin x

0

0

1

cos x

1

x

2

- sin x

0

,x

3

- cos x

-1

x - x3/3!

4

sin x

0

x - x3/3!

5

cos x

1

x - x3/3! + x5/5!

Since the even degree terms are zero, the 2nth Taylor polynomial is the same as the (2n - 1)st. Figure 9.10.2 compares the first and third Taylor polynomials with sin x.

09_infinite_series-688.gif

Figure 9.10.2
Home Infinite Series Taylor's Formula Examples Example 1: Find Taylor Polynomials

Last Update: 2006-11-15