Honors AP Calculus / Mr. Hansen 4/13/2011

Name: _________________________ Bonus (for Mr. Hansen’s use only): ________

Test on Chapter 12 (Calculator for First 15 Minutes)

Rules	You may not write calculator notation anywhere unless you cross it out. For example, fnInt(X^2,X,1,2) is not allowed; write instead. Adequate justification is required for free-response questions. All final answers in free-response portions should be circled or boxed. Decimal approximations must be correct to at least 3 places after the decimal point.
1.	In the subject of statistics (STAtistics), the probability density function for the standard normal curve is given by the function Our goal in parts (b) through (d) will be to estimate f (0.5).
(a)	Write the Maclaurin series (first 3 nonzero terms and general term) for f (x).
(b)	Find an absolute-value error bound for f (0.5) after n nonzero terms. Your answer should be in terms of n, the number of nonzero terms added up. Describe what method you are using (Lagrange, AST, or other), and provide adequate justification. If you need more room, write “OVER.”

(c)	Using the error bound in part (b), determine the number of nonzero terms of part (a) needed to ensure accuracy of f (0.5) within 0.001.
(d)	Use your calculator’s value for f (0.5), namely 0.3520653267643, to determine how many terms of part (a) are actually needed in order to obtain accuracy of f (0.5) within 0.001. Everyone can do this, even those who could not answer parts (b) and (c). Show a little bit of work (a table, perhaps, or a few partial sums if you prefer).
2.	From 2005 AP exam, question #6.
3.	From 2005 Form B AP exam, question #3.