## Jamierox4ev3r one year ago Limits questions

1. 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

2. ganeshie8

finally you have started reviewing epsilon delta!

3. Jamierox4ev3r

Looks like it :P

4. Jamierox4ev3r

I would think you would start off by making this equation: -0.1<5x-5<0.1

5. Jamierox4ev3r

then solving for x -0.1<5x-5<0.1 +5 +5 +5 ------------- 4.9<5x<5.1 /5 /5 /5 --------- 0.98<x<1.02

6. 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?

7. ganeshie8

0.98<x<1.02 thats same as : |x| < 0.02 yes ?

8. Jamierox4ev3r

right

9. ganeshie8

so $$\delta = 0.02$$ works

10. Jamierox4ev3r

so you don't need to subtract from whatever the value of a is? (which in this problem, it's 2)

11. ganeshie8

what that means is if you're with in $$0.02$$ around $$x=2$$, the value of function stays within $$0.1$$ around $$5$$

12. ganeshie8

a graph might help you want to spend some time and see whats going on

13. ganeshie8

or you may continue with rest of the problems and hope things become clear after doing few problems

14. Jamierox4ev3r

It's funny, I've already done a lot of problems. And things seemed pretty straightforward until i got to this one.

15. 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 $$\epsilon =0.1$$

16. 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

17. 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<x<2.002

18. 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.

19. 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

20. ganeshie8

let me ask you a question there

21. Jamierox4ev3r

Sure

22. ganeshie8

you have  1.98<x<2.002  then you say :  from there, I subtracted 2 from 2.02, and 1.98 from two, which both gave me 0.02.

23. Jamierox4ev3r

yes

24. ganeshie8

that is wrong how can both give you 0.02 ? double check

25. Jamierox4ev3r

wait...

26. Jamierox4ev3r

2.02-2=0.02 2-1.98=0.02 ^^ they both do give 0.02 o-o

27. ganeshie8

Oops sry, you're right!

28. ganeshie8

so it seems the same $$\delta$$ works in both cases

29. Jamierox4ev3r

yeah :P weird how the solutions are exactly the same, regardless of the functions being different

30. Jamierox4ev3r

Why is that? do you know?

31. ganeshie8

they both are kinda same functions, they only differ by a constant

32. ganeshie8

f(x) = 5x-5 g(x) = 5x-10

33. Jamierox4ev3r

that's true...I suppose that makes sense, thy only vary by where in the graph they start

34. 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

35. ganeshie8

teamviewer ?

36. Jamierox4ev3r

o-o pardon?

37. ganeshie8

you don't have teamviewer/skype?

38. Jamierox4ev3r

nope

39. Jamierox4ev3r

I could screenshot you what I'm looking at o-o

40. ganeshie8

not necessary, i have a khan academy video that explains exactly this one sec..

41. ganeshie8
42. Jamierox4ev3r

omg @ganeshie8 that's actually a super clear explanation, I got it! Thank you u.u