Question

For the following limit, find the largest δ that works for ε = 0.01 (attached equation)

Answer 1

you want to solve this
\[|\frac{1}{5}x-\frac{5}{7}|<.001 \] for x

Answer 2

sorry

Answer 3

\|[\frac{1}{5}x-\frac{7}{5}|<.001\]

Answer 4

damn!
\[|\frac{1}{5}x-\frac{7}{5}|<.001\]

Answer 5

wat went wrong? u missed some symbol?

Answer 6

the (1/5)x is confusing me

Answer 7

that is what i want. ok finally. we solve easily
\[-.001<\frac{1}{5}x-\frac{7}{5}<.001\]
\[\frac{7}{5}-.001<\frac{1}{5}x<\frac{7}{5}+.001\]
\[7-.005<x<7+.005\]

Answer 8

the last line means
\[|x-7|<.005\] and you are done

Answer 9

I got 1/20

Answer 10

@akileez : u need to find δ such that |x-7|<δ
=> 7-δ<x<7+δ
now use the value from x as given by satellite to find the range of δ.

Answer 11

\[\delta = .005\]and if you replace .001 by \[\epsilon\] you will get
\[\delta= 5\epsilon\]

Answer 12

nice latex brackett! keep it up

Answer 13

that's what I did and I have absolute(x/5-7/5)< 0.01

Answer 14

pulled out 1/5 as common factor which gave me:
absolute(x-7)<5*0.01

Answer 15

ok i was not paying sufficient attention. it should be .01 instead of .001 but you see that it makes no difference at all. you will get .05 instead of .005 no problem

Answer 16

yeah you got it

Answer 17

ok, I see, was jsut a typo - formula was spot on though! so the answer is 1/20?

Answer 18

lines are easy to work with

Answer 19

btw how do you mange to type using all the correct symbols - it"s awesome!

Answer 20

right i used .001 you used .01 you should try it with
\[\epsilon\] and get a general answer

Answer 21

i can show you in chat, but i cannot show you here because they will come up as symbols

Answer 22

if you want come to chat and i can show you the basics easily

Answer 23

sweet, how do I go to chat?