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Math Help - Series and Sequences

  1. #1
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    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.
    Series and Sequences-problem3.jpg

    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
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  2. #2
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    Quote Originally Posted by pham07 View Post
    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.
    Click image for larger version. 

Name:	problem3.jpg 
Views:	6 
Size:	3.1 KB 
ID:	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?
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  3. #3
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    Quote Originally Posted by pham07 View Post
    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.
    Click image for larger version. 

Name:	problem3.jpg 
Views:	6 
Size:	3.1 KB 
ID:	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. \sqrt{e}= e^{\frac{1}{2}}. Put x= 1/2 and then you don't need to find the square root.
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