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Problem 28 Hard 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_1^4 \frac{1}{\sqrt{x}}\ dx $

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Video Transcript

Hey, problem. 28. You need to find a key M. And as it's going to take a crap and the corresponding iris getting to know there's parts, money, Harris and on estimate arrest if you want to find asked him in Paris, you can use this ominous, but it's not you. Months of flying the car, Sonya Aris. It's just I minus, um, or as our teeth. Right. You see that? So you toe fine. He AMs here the function he and and I just do it You know everything. You know what app is on? You know their tax. Just use a function to find PM asked what happens to the Arabs but any stubble? But it's double. You guided the holy interval insuring more pieces. So your approximation is more close to the really mellow. So the arrow's pounds smaller. And if you want to know how to compute, I let me find out. Uh, this one or court acts. Yeah, right. Uh, it is people too, after the negative. Yeah, So we want if I to time. Thanks. When I take a direct hit off this function, it becomes this box. So it's so it's called tow this one, right? It's just, uh two times two minus one is just too right. It's just too it just compute all all those scenes and compare with era.