# Thread: [SOLVED] Prove this limit...

1. ## [SOLVED] Prove this limit...

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

2. 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?

3. ## Thnx

Thanks a lot...

4. ## Question

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

5. 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

6. 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 | |.