Determine a region whose area is equal to $\lim _{n \rightarrow \infty} \sum_{i=1}^{n} \frac{\pi}{2 n} \tan \frac{i \pi}{2 n}$ .
A) $y=\tan x, 0 \leq x \leq \frac{\pi}{3}$
B) $y=\tan x, 0 \leq x \leq \frac{\pi}{5}$
C) $y=\tan x, 0 \leq x \leq \frac{\pi}{6}$
D) $y=\tan x, 0 \leq x \leq \frac{\pi}{4}$
E) $y=\tan x, 0 \leq x \leq \frac{\pi}{2}$

Question

Quizplus · Accepted Answer

The limit represents the Riemann sum for the integral of $\tan x$ from 0 to $\frac{\pi}{2}$.

Determine a Region Whose Area Is Equal To lim⁡n→∞∑i=1nπ2ntan⁡iπ2n\lim _{n \rightarrow \infty} \sum_{i=1}^{n} \frac{\pi}{2 n} \tan \frac{i \pi}{2 n}limn→∞​∑i=1n​2nπ​tan2niπ​

Determine a Region Whose Area Is Equal To $\lim _{n \rightarrow \infty} \sum_{i=1}^{n} \frac{\pi}{2 n} \tan \frac{i \pi}{2 n}$