7172 Evaluate each limit by interpreting it as a Riemann sumin which the given interval

Chapter 5, Problem 71

(choose chapter or problem)

Evaluate each limit by interpreting it as a Riemann sum in which the given interval is divided into $n$ subintervals of equal width.

$\lim \limits_{n \rightarrow+\infty} \sum \limits_{k=1}^{n} \frac{\pi}{4 n} \sec ^{2}\left(\frac{\pi k}{4 n}\right) ;\left[0, \frac{\pi}{4}\right]$

Equation Transcription:

$\lim\limits_{{n} \rightarrow {+\infty{}}}$ $\sum\limits_{k=1}^{n}$ $\frac{\pi{}}{4n}$ sec2 ( $\frac{\pi{}k}{4n}$ ); [0, $\frac{\pi{}}{4}$ ]

Text Transcription:

lim_n right arrow +infinity sum_k=1 ^n pi/4n sec^2 (pi k/4n); [0, pi/4]

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