# Continuity of 1/x

• Nov 19th 2009, 08:38 AM
mtlchris
Continuity of 1/x
Show that 1/x is continuous on at any c =/= 0
hint: chose delta to stay away from 0

i have a general idea of how it works but I'm not really sure how to
"use delta = min{[c]/2,c^2(e/2)} "(answer from book)
• Nov 19th 2009, 11:59 AM
Drexel28
Quote:

Originally Posted by mtlchris
Show that 1/x is continuous on at any c =/= 0
hint: chose delta to stay away from 0

i have a general idea of how it works but I'm not really sure how to
"use delta = min{[c]/2,c^2(e/2)} "(answer from book)

Did you try writing out the definition?

$\displaystyle \left|\frac{1}{x}-\frac{1}{c}\right|=\left|\frac{c-x}{xc}\right|$....how look that the $\displaystyle \delta$. It's $\displaystyle \min$ because obviously we want to restrict our attention so that we may apply some estimation (i.e. on "whatever" neighborhood of c it is always true that "whatever" is less than or equal to "whatever else"). Also, use that in conjunction with the fact that you really only care about bounding $\displaystyle \frac{1}{|xc|}$ for one can make $\displaystyle |c-x|$ as arbitrarily small as one wants.