# approximation with taylor series

• April 27th 2009, 03:19 PM
buttonbear
approximation with taylor series
Over the interval $3 how poorly does the tangent line at $x=4$ approximate $\sqrt {3+x}$? How about the quadratic taylor polynomial?

I'm really not sure of how to approach this one, help please!
• April 29th 2009, 12:03 AM
CaptainBlack
Quote:

Originally Posted by buttonbear
Over the interval $3 how poorly does the tangent line at $x=4$ approximate $\sqrt {3+x}$? How about the quadratic taylor polynomial?

I'm really not sure of how to approach this one, help please!

Start by writing the Taylor polynomials of order 1 and 2 out.

Now there are two approaches one is to use the remainder term for the Taylor series. The second approach is to plot the three functions over the interval (3,5).

CB