[SOLVED] Prove this limit...

**thaliaj_df** · Apr 12th 2009, 09:09 PM

Prove using limit definition:
lim 1/x = 1/c, c is not equal 0
x→ c

**Jhevon** · Apr 12th 2009, 09:17 PM

Originally Posted by thaliaj_df

Prove using limit definition:
lim 1/x = 1/c, c is not equal 0
x→ c

you need to show that for every $\epsilon > 0$ , there is some $\delta > 0$ , such that $|x - c| < \delta$ implies $\left| \frac 1x - \frac 1c \right| < \epsilon$

Now, $\left| \frac 1x - \frac 1c \right| = \left| \frac {c - x}{xc} \right| = \frac {|x - c|}{|xc|}$

Now, can you finish up?

**thaliaj_df** · Apr 12th 2009, 09:26 PM

Thanks a lot...

**thaliaj_df** · Apr 12th 2009, 09:39 PM

I wanted to ask a question though, is it correct to rearrange values of the x and c, it being in absolute brackets.... does it make a difference... Please answer

**mr fantastic** · Apr 12th 2009, 09:39 PM

Originally Posted by thaliaj_df

Prove using limit definition:
lim 1/x = 1/c, c is not equal 0
x→ c

Also asked and replied to here: http://www.mathhelpforum.com/math-he...efinition.html

**mr fantastic** · Apr 12th 2009, 09:42 PM

Originally Posted by thaliaj_df

I wanted to ask a question though, is it correct to rearrange values of the x and c, it being in absolute brackets.... does it make a difference... Please answer

|x - c| = |c - x| by definition of | |.

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[SOLVED] Prove this limit...

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