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anonymous
 4 years ago
Has to do with the epsilondelta definition of a limit. Give me a second to type.
anonymous
 4 years ago
Has to do with the epsilondelta definition of a limit. Give me a second to type.

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anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0Given \[f(x) = 1/ (x1) \] Find \[\delta \] such that if \[0<\left x2 \right<\delta\] then\[\left f(x)1 \right<.01\]

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0I'd appreciate it if you could walk me through how to do it.

myininaya
 4 years ago
Best ResponseYou've already chosen the best response.3\[\frac{1}{x1}1<.01\] => \[.01<\frac{1}{x1}1<.01\] Add 1 to all sides \[1.01<\frac{1}{x1}<1+.01\] \[.99<\frac{1}{x1}<1.01\] \[\frac{99}{100}< \frac{1}{x1}<\frac{101}{100}\] \[\frac{100}{101}<x1<\frac{100}{99}\] Subtract 1 on all sides \[\frac{100}{101}1<x2<\frac{100}{99}1\] \[\frac{100101}{101}<x2<\frac{10099}{99}\] \[\frac{1}{101}<x2<\frac{1}{99}\]

myininaya
 4 years ago
Best ResponseYou've already chosen the best response.3Remember we want \[0<x2<\delta\]

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0Yeah, I think I can take it from here. Just reading through it again :)

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0wait, do we need the absolute values and the zero, then? How do you get those?

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0x−2 >  1/101 then x−2 > 1/101 and x−2<δ ...... therefore δ > 1/101

myininaya
 4 years ago
Best ResponseYou've already chosen the best response.3\[\delta=\frac{1}{101}\] I chose delta to be the smallest

myininaya
 4 years ago
Best ResponseYou've already chosen the best response.3\[x2<\delta => \delta <x2<\delta \]

myininaya
 4 years ago
Best ResponseYou've already chosen the best response.3so since we want the smallest value for delta I chose delta=1/101

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0so the 1/99 doesn't matter then?

myininaya
 4 years ago
Best ResponseYou've already chosen the best response.3no you just want the smallest possible value for delta you can find

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0oh, okay. we kinda skipped through this part in class months ago. hard to review but i think i'm getting the gist of it
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