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Homework Statement
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##.
Homework Equations
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.