11 - Ms. Bony Tighe PDF

Preview

Summary

Ms. Bony Tighe ...

Description

11.11 TAYLOR’S INEQUALITY If

f

( n 1)

( x ) M

for

M x a Rn ( x)  ( n  1)!

x  a d n1

for

, then the remainder x  a d

EX: Approximate the function f ( x )  x by a Taylor polynomial of degree 3 at x = 9 How accurate is this approximation when 8  x  10 ?

Find the Taylor polynomial T3( x) for the function f (x ) sin x at a  4 and  ) How accurate is this approximation on the use it to estimate sin( 46 180 interval 418  x  518 ?

Find the Taylor polynomial

T5 ( x ) for

the function f ( x )  cos x at a  2 and

 use it to estimate cos( 85 180 ) How accurate is this estimation on

80 180

 x  2 ?

Find the Maclaurin polynomial for the function

Find the Taylor polynomial

T5 ( x) for

f (x) 

the function

1 3 x 1

f ( x)  x  1 at a 3

Use the Maclaurin series to compute e0.5 to four non-zero terms.

Use the Maclaurin series to compute e3.5 to four non-zero terms.

Find the Taylor Series f (x ) centered at the given value of a and also find the interval of convergence. f ( x) ln x at a 2

Find the Taylor Series f (x ) centered at the given value of a and also find the interval of convergence. f (x ) 

1 x

at a 4

Use it to approximate

1 3.9

using a third degree Taylor Polynomial.

How accurate is this approximation on the interval

x 4

Use a third degree Taylor Polynomial to approximate

1

f ( x ) tan(0.5)...