The Idea of a Limit

But some limits aren’t at zero!

•Instead of “y approaches zero as x approaches zero,” we will need to say “y approaches L as x approaches c.”

•Instead of |y| < e, we will need to write |y – L| < e.

•Instead of 0 < |x| < d, we will write 0 < |x – c| < d.

“The limit, as x approaches c, of y, is L.”

This is true when:

For any e > 0,

there exists a d > 0 such that

whenever 0 < | x – c | < d,

we will have | y – L | < e.