# Homework Help: Epsilon Delta

1. Apr 13, 2013

### Zondrina

1. The problem statement, all variables and given/known data

Suppose f is a function defined on a set $S$ in $ℝ^n$ and suppose $Q$ is a limit point of $S$.

If $f(P) → 3$ as $P → Q$ prove from first principles that $\frac{1}{f(P)} → \frac{1}{3}$ as $P → Q$.

2. Relevant equations

3. The attempt at a solution

I'm a bit rusty with these.

I know : $\forall ε'>0, \exists δ'>0 \space | \space 0 < |P-Q| < δ' \Rightarrow |f(P) - 3| < ε'$

I want : $\forall ε>0, \exists δ>0 \space | \space 0 < |P-Q| < δ \Rightarrow |1/f(P) - 1/3| < ε$

For some reason I'm blanking on what to do next.

2. Apr 13, 2013

### tiny-tim

HI Zondrina!

Hint: |1/f(P) - 1/3| = |f(P) - 3| / |f(P)|

3. Apr 13, 2013

### Zondrina

Thanks tim, cleaned up nicely :)