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Westview High School

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Problem 38

Finding a $\delta$ for a Given $\varepsilon$ Repeat Exercise 37 for $\varepsilon=0.05,0.01,$ and $0.005 .$ What happens to the value of $\delta$ as the value of $\varepsilon$ gets smaller?

Answer

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## Discussion

## Video Transcript

for giving the following function after VAX is equal to two minus one over X, where it's just determined us. Based off of the values of 0.5 0.1 Zero point 005 So to start off with, we know that he is based off of the white access. So the first thing we need to do yes, we need to take this function and we need to make it. We need find Empress of it. So basically, we need to stop access it. Otherwise, the first well do you think of FX was a Y is equal to two nice one over X so you can slip it to get X is equal to two minus y over. Why we can I won over wide to one side so we can add one over wide to both sides. Then subtract Becks to get us one over. Why is he going to minus X? And then we can multiply by wind from both sides to get one is you go to white times to my sex. We divide us, says, or to my sex to get us. Why is equal to one over to my sex, so you know, that is the inverse That's difficult to one over to my six. So now we're giving us information when we just start plugging different values of E. So we start with let's say that we have the is equal to 0.5 so you can plug into our function. So we get, like the one of acts now would have to be both the positive and the negative aspects. In this case of the positive aspect. First have a one over. So then we have two minus this over in verse. And then we know that the limb approaches one. So we have one plus 0.5 which is equal to plenty over 19 and then it We also have to look at the negative aspect. So we have one over Tu minus one minus 0.5 which gets us 20/21. And based off with this information, we know that there s value. He redraw that his family is equal to 1/21 because it's a minimum and we have to go based off of the inverse of negative because it's kind of like represents a wide valley. Okay, so now we have to do to repeat it for their 0.1 So we have once again would do the same exact thing, but neither one of explosive, which is one over Tu minus one plus their points or one which will get us 100 over 99. And then we have to repeat the same thing for negative. We have 1/2, my ass. One might 0.1 just equal to. But how? That we were one on one. You know, actually, you is equal to 100. Sorry. Which is equal to one over 101. All right. Now we have to repeat this for e his equal chick 0.5 So the plug that in one. So in verse. Positive. So you get 12 plus one plus of points. There is over five, which gets you 200 for 1 99 and then you have to do the same. Front. Negative and verse gets you chew loops. That should over here should be a minus. Tu minus 110.5 Which gets you 200 over to one. So you know, that s a little is equal to one over 201. So we noticed that I was r e Value decreases SAR e value decreases. Over. Here was your evils decreases. We can also see what happens. There s Ali will also decreases.