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