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Guess the value of the limit (if it exists) by evaluating the function at the given numbers (correct to six decimal places).$\lim _{x \rightarrow \pi^{-}} \cot x$

$-\infty$

Calculus 1 / AB

Chapter 2

Limits

Section 3

Limits of Functions at Finite Numbers

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everybody. Chapter two, Section three Problem 34. This one won't take too long. This one is a snap. So we're talking about Ah, the limit as X approaches Pi fromthe left of co tangent of X. So the most important thing that you need to know about this is that CO tangent is co sign over sign And when we have sign at pie, that is zero. So we have co sign of X over sign of X when you're at pie, right? Satoko san. A pie is negative. One sign of pi zero You have negative one of zero so undefined, which means that you have a vertical ass in tow, which means that at this value of pi rights were blowing up. And if we're approaching it from the left, which is what this minus means, that means that where were blown up, we're either gonna blow down or we're gonna blow up, and I need to know which one. So if we're just a normal coach, Hank, a graph, if we're blowing up, were positive. And if we're blowing down, we are negative. So all I mean to dio is I need to find something that is just a little bit less than pie, and I need to find out if it's positive or negative, and then that will tell us the story. So let's plug in something that's less than pie, which is about 3.14 So let's plug in like 2.5, right. We need to get in between discontinuities, and there's another just continuity at zero. So we just need to make sure to be in between zero and pi so that we can get an accurate read out of this thing. And so I want to. I want to be a pretty close to pie. Make sure we don't jump over, you know, any access. So if we pick something like 2.5, right, let's pick something that's really, really, really close. Then if we plug into a 0.5 to this thing, we get co signed of 2.5, and keep in mind that I am gonna be doing this in radiance because it's talking about pie. So I want to do this. It radiance. So if it's gonna be in the bottom, we need a negative. It's gonna be the top When you deposited Phillips it would get if you plug it into a calculator and you get co tangent. 2.5. Then you get something that is approximately negative. 1.3. And so that's a negative number. So that means that it here, we live in a negative space, which means this thing is going to go down. And that means that the limit of this thing is we go from the left side is going to be negative. Infinity! There you go. Help that help until next time.

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