Been doing some calculus review to knock the rust off for this coming fall semester and I got stuck...(adsbygoogle = window.adsbygoogle || []).push({});

1. The problem statement, all variables and given/known data

From Stewart's book (Early Transcendentals: 6E): (7.8 pg517 #69)

Determine how large the number "a" has to be so that:

[itex]\int[/itex][itex]\stackrel{\infty}{a}[/itex][itex]\frac{1}{x^{2}+1}[/itex]dx <.001

2. Relevant equations

None.

3. The attempt at a solution

Ok, I can easily picture the graph and the area under it. I figured I'd integrate, use "a" for my lower bound and "t" for the upper bound, then by using the potential equation it's just a simple matter of solving for "a" while taking the limit of said equation as t goes to infinity.

I managed to get:

(I suck at "latex" but this should technically bearctan (t) - arctan (a) < 1/1000the limitof those arctans as t -> infinity < .001)

Here is where I think I'm screwing up... I take the tangent of both sides:

- and I'm stuck, I know I can't just apply the tangent function independently to both parameters giving metan [arctan t -arctan a] < tan (1/1000)t - a < tan (.001)is there some trig identity I'm not thinking of..?

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# Improper Integral (Calc II)

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