Limits

Tonight, I was reading about the fundamental definition of limits of functions, and for the first time, really understood it.  The context was a limit in multiple variables, as

\displaystyle\lim_{(x,y)\to (0,0)}f(x,y) = L

The interesting issue is that in two dimensions like this, showing the limit exists is harder than one dimensions, since there are infinitely many ways to approach (a,b).   The definition for continuity becomes, f(x,y) is continuous at the point (a,b) if the limit exists and is f(a,b) , or

\displaystyle\lim_{(x,y)\to (a,b)}f(x,y) = f(a,b)

Somehow, I never fully understood the 1D case until I saw the explaination and example in 2D.

Advertisements
Explore posts in the same categories: Math

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s


%d bloggers like this: