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 cos1 (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 cos1 x . 1...
View
Full Document
 Fall '07
 McClain
 Calculus, Addition, Taylor Series, upper bound, Logarithm, polynomial expansion, David Howard

Click to edit the document details