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Calculus II

by: Reuben Hudson DDS

Calculus II MATH 132

Reuben Hudson DDS
GPA 3.55

Thurlow Cook

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Thurlow Cook
Class Notes
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This 1 page Class Notes was uploaded by Reuben Hudson DDS on Friday October 30, 2015. The Class Notes belongs to MATH 132 at University of Massachusetts taught by Thurlow Cook in Fall. Since its upload, it has received 17 views. For similar materials see /class/232217/math-132-university-of-massachusetts in Mathematics (M) at University of Massachusetts.

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Date Created: 10/30/15
In nite Series convergence tests is it geometric Ifso ifthe absolute value ofr is less than 1 it converges Limit divergence test 7 if the limit of the general term as the index goes to in nity does not equal zero the series diverges Comparison test 1 for positive series 7 if the general term is always less than or equal that of another series and the other series converges then your series converges In the same way if the general term is always greater than or equal to that of another series and the other series diverges then your series diverges Comparison test 2 for positive series7 if the limit as the index goes to in nity of your series divided by another series equals some nite positive number L then both series must either converge or both diverge If for all n gt 1 fn an and f is positive continuous and decreasing then the series of an and the integral from 1 to in nity of an either both converge or both diverge Pseries test 7 if your series is a pseries ifp is greater than 1 the series converges pr is less than or equal to l the series diverges Ratio test 7 let L the limit as the index goes to in nity of the absolute value of the nlth term divided by the nth term IfL is less than 1 the series converges If L is greater than 1 it diverges If L l the test is inconclusive and you must use a di erent test absolute convergence 7 if the series of the absolute value of the general term converges then the series of the general term also converges The series is said to converge absolutely Taylor series 7 any function fx can be represented by a speci c in nite series centered at c of the form M Z quot0 111 quotc x 7 cquot 7 fx this is called the Taylor series When c 0 this is also called the Maclaurin series


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