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Problem 27 Medium Difficulty

Find the approximations $ T_n $, $ M_n $, and $ S_n $ for $ n = 6 $ and 12. Then compute the corresponding errors $ E_T $, $ E_M $, and $ E_S $. (Round your answers to six decimal places. You may wish to use the sum command on a computer algebra system.) What observations can you make? In particular, what happens to the errors when $ n $ is doubled?

$ \displaystyle \int_0^2 x^4\ dx $

Answer

4 as $n$ is doubled.
16 as $n$ is doubled.

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Video Transcript

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