Question

Limits questions

Answer 1

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

Answer 2

finally you have started reviewing epsilon delta!

Answer 3

Looks like it :P

Answer 4

I would think you would start off by making this equation:

-0.1<5x-5<0.1

Answer 5

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

Answer 6

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?

Answer 7

0.98<x<1.02

thats same as :

|x| < 0.02

yes ?

Answer 8

right

Answer 9

so \(\delta = 0.02\) works

Answer 10

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

Answer 11

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

Answer 12

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

Answer 13

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

Answer 14

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

Answer 15

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 \(\epsilon =0.1\)

Answer 16

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

Answer 17

^ 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

Answer 18

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.

Answer 19

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

Answer 20

let me ask you a question there

Answer 21

Sure

Answer 22

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.`

Answer 23

yes

Answer 24

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

Answer 25

wait...

Answer 26

2.02-2=0.02
2-1.98=0.02

^^
they both do give 0.02 o-o

Answer 27

Oops sry, you're right!

Answer 28

so it seems the same \(\delta\) works in both cases

Answer 29

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

Answer 30

Why is that? do you know?

Answer 31

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

Answer 32

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

Answer 33

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

Answer 34

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

Answer 35

teamviewer ?

Answer 36

o-o pardon?

Answer 37

you don't have teamviewer/skype?

Answer 38

nope

Answer 39

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

Answer 40

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

Answer 41

here is it is
https://www.khanacademy.org/math/differential-calculus/limits_topic/epsilon_delta/v/epsilon-delta-limit-definition-1

Answer 42

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