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AddendumtestIIc2 - can be for our polynomial expansion It...

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Addendum David Howard 11 February 2009 This question is due at the start of Class tomorrow Thursday February 12. You may work together but you may not ask any members outside of our class 1501B1/B2/B3. Additionally, the write up for the question must be ON YOUR OWN, no other member in class may look over or copy any part of your write-up. Any cheating found on this assignment will be considered cheating on the test and I will report you to the Office of Student Integrity. Also I would recommend using a calculator whether it be your own or online, but SHOW YOUR WORK!!!. Also I am talking about the cosine inverse function here. 1. (a) (9 points) Find the Taylor series polynomial expansion of cos - 1 x using the power series in terms of x up to the x 6 term. (Note: this whole problem is in RADIANS! not degrees.) (b) (2 points) Find the value given by your polynomial for cos - 1 (0 . 3).(Round to 5 decimal places.) (c) (9 points) The Lagrange Formula gives us an upper bound on how bad our estimate
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Unformatted text preview: can be for our polynomial expansion. It says the worst possible error in our estimate is no more than max c ∈ [0 , . 3] ± ± ± ± f ( n +1) ( c ) ( n + 1)! x n +1 ± ± ± ± where max c ∈ [0 , . 3] is the c that maximizes the expression to the right in the given interval. Find this upper bound for our error in estimating cosine inverse of 0 . 3. (Hint: The maximum c is at [0 . 3] and you don’t have to show why c = 0 . 3. Again, round to the nearest 5th decimal place.) If you type into the calculator and see the difference in error for cos-1 (0 . 3) you should see the actual error is a lot smaller than the upper bound error. Also I encourage students with a graphing calculator to look at the difference between the Taylor polynomial you found and the actual graph of cos-1 x . 1...
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