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Problem 45

Using the $\varepsilon$ -\delta Definition of Lim…

Problem 44

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 $(b) \varepsilon=0.005 .$
$$\lim _{x \rightarrow 3} x^{2}$$


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Video Transcript

were given a limit as X approaches. Serie of X squared. So who pulled in three for X squared were lost with We know the limit purchased night Place off for this week. Rick. We know front for part A. We're giving the value 0.1 so price offer this week in creator inequality. So we're left with doubts about Xcor. Last thing. It's lost some 0.1 you can factor about swords. Optional extra. My street. It's absolutely export. Serie Boston 0.1 which we can simplify down to three. Don't lose value X mystery. Listen, Jo, point your awards after Laura Xmas Tree is bustem 0.0 warned over three based off of this information in a daughter, it's equal to to a 0.0 1/3. Um, for part B, we're giving a different value. So we have. The value is equal to 0.5 So place officer relation. It's the same steps just earlier, except using the number zero point. There's are a fraction of the explosion. Serie Jackson was out of explosive. Three. Looks a little pointers there. Five. Black out Your doctor. It down, right? And so then we are left with. So a lot of extra nursery is lost in 0.5 or three? No. And I felt I was equal. Just a lot of ex my stage over. Delta go up to 0.543