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Problem 26

(a) Use Definition 2 to find an expression for th…

Problem 25

Determine a region whose area is equal to the given limit. Do not evaluate the limit.

$ \displaystyle \lim_{n \to \infty} \sum_{i = 1}^{n} \frac{\pi}{4n} \tan{\frac{i \pi}{4n}} $


This sum represents the area under the curve $y=\tan x$ and above
$x$ -axis in the interval $x \in\left[0, \frac{\pi}{4}\right]$


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Video Transcript

okay. We know the formula for Delta X er change in Axis B minus a divide by an Given the limit that the problems given us, we know Delta axes pi over four on and a zero. Therefore, if Delta Axe is be minus a over and then it's and demonized over an is equivalent to pi over four end, then we actually condone drive a value for B we get B is equivalent to pi over four. Therefore, what we know is that we end up with the same limit that if the integral from zero to fought for of tan of axe DX mean the sum represents the area under the curve. Reichel's 10 of X and above the X axis in the interval, x from 0 to 4 pi over four.

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