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lbl 2 lcl 2 sin 2 θ
Proof of Alternating Series Test With no loss of generality we can assume that the series begins at n =1. If not we could change the proof below to meet the new starting place
Steps for Alternating Series Test Suppose that we have a series ∑a n and either a n = (-1) n b n or a n = (-1) n+1 b n where b n > 0 for all n. Then if, 1.
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methodology of OR
Logarithmic Differentiation : There is one final topic to discuss in this section. Taking derivatives of some complicated functions can be simplified by using logarithms. It i
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Assume that (xn) is a sequence of real numbers and that a, b € R with a is not eaqual to 0. (a) If (x n ) converges to x, show that (|ax n + b|) converges to |ax + b|. (b) Give
A solid is formed by cutting the top off of a cone with a slice parallel to the base, and then cutting a cylindrical hole into the resulting solid. Determine the volume of the holl
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