Jamierox4ev3r
  • Jamierox4ev3r
Limits questions
Mathematics
  • Stacey Warren - Expert brainly.com
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katieb
  • katieb
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Jamierox4ev3r
  • Jamierox4ev3r
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
ganeshie8
  • ganeshie8
finally you have started reviewing epsilon delta!
Jamierox4ev3r
  • Jamierox4ev3r
Looks like it :P

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Jamierox4ev3r
  • Jamierox4ev3r
I would think you would start off by making this equation: -0.1<5x-5<0.1
Jamierox4ev3r
  • Jamierox4ev3r
then solving for x -0.1<5x-5<0.1 +5 +5 +5 ------------- 4.9<5x<5.1 /5 /5 /5 --------- 0.98
Jamierox4ev3r
  • Jamierox4ev3r
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?
ganeshie8
  • ganeshie8
0.98
Jamierox4ev3r
  • Jamierox4ev3r
right
ganeshie8
  • ganeshie8
so \(\delta = 0.02\) works
Jamierox4ev3r
  • Jamierox4ev3r
so you don't need to subtract from whatever the value of a is? (which in this problem, it's 2)
ganeshie8
  • ganeshie8
what that means is if you're with in \(0.02\) around \(x=2\), the value of function stays within \(0.1\) around \(5\)
ganeshie8
  • ganeshie8
a graph might help you want to spend some time and see whats going on
ganeshie8
  • ganeshie8
or you may continue with rest of the problems and hope things become clear after doing few problems
Jamierox4ev3r
  • Jamierox4ev3r
It's funny, I've already done a lot of problems. And things seemed pretty straightforward until i got to this one.
Jamierox4ev3r
  • Jamierox4ev3r
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 \(\epsilon =0.1\)
ganeshie8
  • ganeshie8
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
Jamierox4ev3r
  • Jamierox4ev3r
^ 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
Jamierox4ev3r
  • Jamierox4ev3r
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.
Jamierox4ev3r
  • Jamierox4ev3r
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
ganeshie8
  • ganeshie8
let me ask you a question there
Jamierox4ev3r
  • Jamierox4ev3r
Sure
ganeshie8
  • ganeshie8
you have ``` 1.98
Jamierox4ev3r
  • Jamierox4ev3r
yes
ganeshie8
  • ganeshie8
that is wrong how can both give you 0.02 ? double check
Jamierox4ev3r
  • Jamierox4ev3r
wait...
Jamierox4ev3r
  • Jamierox4ev3r
2.02-2=0.02 2-1.98=0.02 ^^ they both do give 0.02 o-o
ganeshie8
  • ganeshie8
Oops sry, you're right!
ganeshie8
  • ganeshie8
so it seems the same \(\delta\) works in both cases
Jamierox4ev3r
  • Jamierox4ev3r
yeah :P weird how the solutions are exactly the same, regardless of the functions being different
Jamierox4ev3r
  • Jamierox4ev3r
Why is that? do you know?
ganeshie8
  • ganeshie8
they both are kinda same functions, they only differ by a constant
ganeshie8
  • ganeshie8
f(x) = 5x-5 g(x) = 5x-10
Jamierox4ev3r
  • Jamierox4ev3r
that's true...I suppose that makes sense, thy only vary by where in the graph they start
Jamierox4ev3r
  • Jamierox4ev3r
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
ganeshie8
  • ganeshie8
teamviewer ?
Jamierox4ev3r
  • Jamierox4ev3r
o-o pardon?
ganeshie8
  • ganeshie8
you don't have teamviewer/skype?
Jamierox4ev3r
  • Jamierox4ev3r
nope
Jamierox4ev3r
  • Jamierox4ev3r
I could screenshot you what I'm looking at o-o
ganeshie8
  • ganeshie8
not necessary, i have a khan academy video that explains exactly this one sec..
ganeshie8
  • ganeshie8
here is it is https://www.khanacademy.org/math/differential-calculus/limits_topic/epsilon_delta/v/epsilon-delta-limit-definition-1
Jamierox4ev3r
  • Jamierox4ev3r
omg @ganeshie8 that's actually a super clear explanation, I got it! Thank you u.u

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