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### Finding a $\delta$ for a Given $\varepsilon$ In E…

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Problem 40

Finding a $\delta$ for a Given $\varepsilon$ In Exercises $39-44,$ find the limit $L .$ Then find $\delta$ such that $|f(x)-L|<\varepsilon$ whenever $0<|x-c|<\delta$ for (a $)$ $\varepsilon=0.01$ and $(b) \varepsilon=0.005 .$

$$\lim _{x \rightarrow 6}\left(6-\frac{x}{3}\right)$$

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## Video Transcript

were given a falling limit on your ass to find us probably given following a valley. So for part A were given that who is equal to 0.1 All right, so it's a start off with. We can make our inequality so you have the absolute value of six X oversee minus four in their e value. So it's lost 0.1 We can simplify this down to perhaps a volley of six minus X nursery, which is equal to the absolute value of X minus six over Serie. This loss hurt 2.1 And if we monster car by three, we get the absolute value of X, my six sauced in 0.3 So now we can solve the inequality. So we have X minus six that was lost in 0.3 which leaves us with see of 66 plus through 0.3 And then if we do six miles socks less than 0.3 Well, off with yeah, six. My 0.0 sway 0.3 six eso Obviously we can forget the solution by unionizing different. So the different questions I would just created race off this information. You can exclude sex, and we know that the SA Lou, it's equal to 0.3 We're partly we can apply the same logic. Except this time our values different only have 0.5005 Okay, So once again we have you to say is I think so. We have the same Zach Absolute valley, our own. So we have. That's a value of six. My sex or three mice war most in 0.1 So that some flight down my attacks over three you call two X minus six weeks sauce. Is there a point? Sorry, we're not using 2.1 Were using 0.5 lots of Pardubice rates were left with after about acts. My six last 10 SharePoint share one fire in so than we can solve for both sides of ax minus six loss and 0.15 six months Explosive. 0.0 five. We're lost worth 66 closer Quite true. 15 and then 610.156 Yet we can unionize that you equations that we've got in India or the sixties You also asked is equal to 0.1