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Get a Patch! Social Media. Connect With Us! Then xC1 x. Note that x D 1 is not a critical point because it is not in the domain of f. As x increases through 2, f 0. As x increases through 0, f 0. Though f 0. As x increases through 1, f 0.
On the other hand, as x increases through 1, f 0. Find the area of the region enclosed by the graphs of f. For the endpoint x D 2 e 1, the series becomes. Thus, the series e. For the endpoint x D 3, the series becomes X1 X1 1 1 2 , which converges by the Limit Comparison Test comparing with the convergent p-series. For the endpoint. Thus, the series converges for.
In Exercises 35—40, use Eq. Thus, we first compute the integral of each com- ponent. Thus, we first compute the integral of each component.
For the second integral we use the substitution t D 1 C s 2 , dt D 2s ds. Introduction to Real Analysis by William F.
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