# Thread: approximation with taylor series

1. ## approximation with taylor series

Over the interval $\displaystyle 3<x<5,$ how poorly does the tangent line at $\displaystyle x=4$ approximate $\displaystyle \sqrt {3+x}$? How about the quadratic taylor polynomial?

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

2. Originally Posted by buttonbear
Over the interval $\displaystyle 3<x<5,$ how poorly does the tangent line at $\displaystyle x=4$ approximate $\displaystyle \sqrt {3+x}$? 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