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Limits/continuity  finding largest delta 
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#1
Apr112, 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! 


#2
Apr112, 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 =] 


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