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Proof Prove that if the limit of $f(x)$ as $x$ ap…

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Problem 80

Evaluating Limits Use a graphing utility to evaluate

$$\lim _{x \rightarrow 0} \frac{\tan n x}{x}$$

for several values of $n .$ What do you notice?

We notice that the limit is equal to $n$ in each case

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Video Transcript

So we're giving the following them as actual approaches era of 10 10 and X over X, where I need some sort of constantly asked you so some sort graphing utility is so in this case, I'm just needs done does most. I want to see what llamas expert to zero is. So if we have, um, our function and so let's say we sat under sickle to one, we can see that the limits experts zero seems to converge on what now let's move up the values of Ansel's so it to 20 when consider the limit seems to approach to this, time went and is able to to reset to three. We can see that the limit as expertise. Air of the function also seems to post three, and once again we do, for you can see the limit. Those X approaches, so of were an is equal to four seems also be approaching for so myself. Of this information, you seem to see a pattern where every single time you change the value of N that is it has the same value as a limit. So myself, the separation there's awful graphing it. We can say that we noticed that the limit as experts zero off Tan Teoh end to the X over X is equal to, huh?