# Series and Sequences

• Dec 8th 2009, 05:42 PM
pham07
Series and Sequences
Use the 3rd degree polynomial for e^x to estimate sqrt of e (4 decimal places). Find, and justify, an upper bound in error.

I know what e^x is as an expansion.
Attachment 14358

I know to go up to the 3rd degree, fine. To estimate the square root of e, would I just plug in 1 into the equation and then take the square root of the sum of the numbers? For the upper bound I know to use taylor's remained theorem
• Dec 8th 2009, 08:20 PM
Prove It
Quote:

Originally Posted by pham07
Use the 3rd degree polynomial for e^x to estimate sqrt of e (4 decimal places). Find, and justify, an upper bound in error.

I know what e^x is as an expansion.
Attachment 14358

I know to go up to the 3rd degree, fine. To estimate the square root of e, would I just plug in 1 into the equation and then take the square root of the sum of the numbers? For the upper bound I know to use taylor's remained theorem

Sounds like you know what you're doing, so what's the problem?
• Dec 9th 2009, 05:42 AM
HallsofIvy
Quote:

Originally Posted by pham07
Use the 3rd degree polynomial for e^x to estimate sqrt of e (4 decimal places). Find, and justify, an upper bound in error.

I know what e^x is as an expansion.
Attachment 14358

I know to go up to the 3rd degree, fine. To estimate the square root of e, would I just plug in 1 into the equation and then take the square root of the sum of the numbers? For the upper bound I know to use taylor's remained theorem

Square root is 1/2 power. $\displaystyle \sqrt{e}= e^{\frac{1}{2}}$. Put x= 1/2 and then you don't need to find the square root.