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Express As a Definite Integral, Then Find the Limit

question 81

Essay

Express limn{i=1n[cos(πin)]πn}\lim _ { n \rightarrow \infty } \left\{ \sum _ { i = 1 } ^ { n } \left[ \cos \left( \frac { \pi i } { n } \right) \right] \frac { \pi } { n } \right\} as a definite integral, then find the limit.

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Definitions:

Jeopardy

A situation involving exposure to danger, risk, or harm.

Skepticism

An attitude of doubt or a disposition to incredulity either in general or toward a particular object.

Heuristics

Are simplifying strategies or “rules of thumb” used to make decisions.

Certainty

The total absence of doubt about something.

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