Register to reply

Limits/continuity - finding largest delta

by roman93
Tags: delta, largest, limits or continuity
Share this thread:
roman93
#1
Apr1-12, 05:06 PM
P: 14
Hey guys, I found this question and it started bugging me:

find the _largest_ δ such that |x - 5| < δ => |1/x - 1/5| < 1/100.

This is what I did to try solve the question:

From |1/x - 1/5| < 1/100 : I got 1/x > 19/100 and so I wanted x < 100/19
plugging that back into the first inequality it gave δ = 5/19

But I don't think what I did is right because when I was trying values for x which satisfied this it gave answers which were over 1/100.

So my question is how would I solve this type question.
Any help is very much appreciated :)

Thank you in advance!
Phys.Org News Partner Science news on Phys.org
Bees able to spot which flowers offer best rewards before landing
Classic Lewis Carroll character inspires new ecological model
When cooperation counts: Researchers find sperm benefit from grouping together in mice
roman93
#2
Apr1-12, 05:16 PM
P: 14
I think I know where I went wrong, what I should be doing is finding an upper bound for 1/x rather than a lower bound. The answer I now have is 5/21 and this seems to work.

If I have gone wrong somewhere, please do point it out =]


Register to reply

Related Discussions
Limits and Continuity Calculus & Beyond Homework 6
Epsilon and delta method of finding limits? Calculus & Beyond Homework 7
Continuity, but is it limits or delta-epsilon or neighborhood? Calculus & Beyond Homework 1
Help please! delta - epsilon.. continuity Calculus & Beyond Homework 0
Epsilon-delta continuity Calculus 3