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algebraic continuity theorem


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#1 BMAD

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Posted 12 November 2013 - 11:30 PM

I am helping a friend in introductory real analysis, someone please help me finish, I am stuck.

Want to show that f(x)/g(x) is continuous as x goes to c given that g© is not 0.

|f(x)/g(x) - f©/g©| = |1/(g(x)g©)||f(x)g©-f©g(x)| = |1/(g(x)g©)||f(x)g©-f©g(x)-f(x)g(x) + f(x)g(x)| <= |1/(g(x)g©)||f(x)||g(x)-g©| + |g(x)||f(x)- f©|

Then I draw a Blank.
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#2 BMAD

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Posted 13 November 2013 - 12:11 AM

Found my mistake !
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#3 bonanova

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Posted 07 July 2014 - 01:52 AM

Hi BMAD,

 

Hint, to keep ( c ) from turning into © you can insert spaces, or use [c] as a substitute.

 

Are there others?

 

(a) (b) © (d) (e) (f) (g) (h) (i) (j) (k) (l) (m) (n) (o) (p) (q) ® (s) (t) (u) (v) (w) (x) (y) (z)

 

( c ) ( r )


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The greatest challenge to any thinker is stating the problem in a way that will allow a solution.
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#4 BMAD

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Posted 26 July 2014 - 05:16 AM

I appreciate it.


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