Thread: [SOLVED] Prove this limit...

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

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 $\displaystyle \epsilon > 0$, there is some $\displaystyle \delta > 0$, such that $\displaystyle |x - c| < \delta$ implies $\displaystyle \left| \frac 1x - \frac 1c \right| < \epsilon$

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

Now, can you finish up?

Thanks a lot...

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

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

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 | |.