Truncation Error in Taylor Series

function

e

x

sin(x)

cos(x)

number of terms

5

x value

1.2

5

10

15

20

n

-2

-1

1

2

error

approximate value =	3.29440000
exact value =	3.32011692
truncation error =	0.02571692

Taylor series for transcendental functions have an infinite number of terms. This Demonstration shows the truncation error created by using a finite number of terms in approximating three such functions with Taylor series based at zero.