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Given that \[\lim_{x \rightarrow 2}(5x-5) =5\], find values of \(\delta\) that correspond to \(\epsilon\)=0.1, \(\epsilon\)=0.05, and \(\epsilon\)=0.01
finally you have started reviewing epsilon delta!
Looks like it :P

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Other answers:

I would think you would start off by making this equation: -0.1<5x-5<0.1
then solving for x -0.1<5x-5<0.1 +5 +5 +5 ------------- 4.9<5x<5.1 /5 /5 /5 --------- 0.98
I'm just kind of confused as to what you would do here... Since a=2, wouldn't you subtract 0.98 and 1.02 from 2?
0.98
right
so \(\delta = 0.02\) works
so you don't need to subtract from whatever the value of a is? (which in this problem, it's 2)
what that means is if you're with in \(0.02\) around \(x=2\), the value of function stays within \(0.1\) around \(5\)
a graph might help you want to spend some time and see whats going on
or you may continue with rest of the problems and hope things become clear after doing few problems
It's funny, I've already done a lot of problems. And things seemed pretty straightforward until i got to this one.
For example, I had a problem that read, "Find a number \(\delta\) such that if \[\left| x-2 \right|=\delta\], then \(\left| 5x-10\right|=\epsilon\), where \(\epsilon =0.1\)
ikr! often times the concepts look so easy when you read them but you only get to really learn them only after actually solving the problems
^ agreed. But this problem that preceded...I was able to get it with no problem. my process looked like this: -0.1<5x-10<0.1 +10 +10 +10 ------------------ 9.9<5x<10.1 /5 /5 /5 ---------- 1.98
from there, I subtracted 2 from 2.02, and 1.98 from two, which both gave me 0.02. So I concluded that \(\delta =0.02\), which was a correct answer according to the computer software I'm using.
So I assumed from then that I knew what I was doing XD I suppose I was just confused about the fact that the functions are different, but they wield the same answers
let me ask you a question there
Sure
you have ``` 1.98
yes
that is wrong how can both give you 0.02 ? double check
wait...
2.02-2=0.02 2-1.98=0.02 ^^ they both do give 0.02 o-o
Oops sry, you're right!
so it seems the same \(\delta\) works in both cases
yeah :P weird how the solutions are exactly the same, regardless of the functions being different
Why is that? do you know?
they both are kinda same functions, they only differ by a constant
f(x) = 5x-5 g(x) = 5x-10
that's true...I suppose that makes sense, thy only vary by where in the graph they start
Another thing i don't get is that with the 5x-10, you use 2 in order to find \(\delta\) but with 5x-5, you use 1 in order to find \(\delta\) I don't know why I get hung up on these tiny details XD
teamviewer ?
o-o pardon?
you don't have teamviewer/skype?
nope
I could screenshot you what I'm looking at o-o
not necessary, i have a khan academy video that explains exactly this one sec..
here is it is https://www.khanacademy.org/math/differential-calculus/limits_topic/epsilon_delta/v/epsilon-delta-limit-definition-1
omg @ganeshie8 that's actually a super clear explanation, I got it! Thank you u.u

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