- #1

miren324

- 14

- 0

Let f:D-

**R**and c in

**R**be and a accumulation point of D, which is a subset of

**R**. Suppose that a<=f(x)<=b for all x in D, x not equal to c, and suppose that limx[tex]\rightarrow[/tex]c f(x) = L. Prove that a<=L<=b.

I'm having trouble here. I've tried to prove by contradiction, by assuming that L<a, then after a contradiciton, assuming L>b. This led through a lot of junk and I ended up back where I started. I am unsure how to construct a proof using the analogous relationship of sequences and functions.

Any help would be greatly appreciated.