Use procedure to find Taylor polynomial of degree 4 for sinx with a=pi/4.
Favorites|Homepage
Subscriptions | sitemap
HOME > > Use procedure to find Taylor polynomial of degree 4 for sinx with a=pi/4.

Use procedure to find Taylor polynomial of degree 4 for sinx with a=pi/4.

[From: ] [author: ] [Date: 11-11-28] [Hit: ]
- (√2/2)(x - π/4)^3/3! + (√2/2)(x - π/4)^4/4!.Since this is a series in radians, note that 50º = 50π/180 = 5π/18.Now,......
Use procedure to find Taylor polynomial of degree 4 for f(x) = sinx with a = pi/4. Use the result to approximate sin 50º.

Thanks for help!

-
Using the definition:
f(x) = sin x ==> f(π/4) = √2/2
f '(x) = cos x ==> f '(π/4) = √2/2
f ''(x) = -sin x ==> f ''(π/4) = -√2/2
f '''(x) = -cos x ==> f '''(π/4) = -√2/2
f ''''(x) = sin x ==> f ''''(π/4) = √2/2

Hence, sin x
≈ √2/2 + (√2/2)(x - π/4) - (√2/2)(x - π/4)^2/2! - (√2/2)(x - π/4)^3/3! + (√2/2)(x - π/4)^4/4!.

Since this is a series in radians, note that 50º = 50π/180 = 5π/18.
Now, substitute x = 5π/18 for the desired approximation.

I hope this helps!
1
keywords: with,of,find,sinx,for,4.,pi,Taylor,procedure,degree,Use,to,polynomial,Use procedure to find Taylor polynomial of degree 4 for sinx with a=pi/4.
New
Hot
© 2008-2010 http://www.science-mathematics.com . Program by zplan cms. Theme by wukong .