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## Homework Statement

Define: f(z) [tex]\rightarrow[/tex] w1 as z [tex]\rightarrow[/tex] z0

and

g(z) [tex]\rightarrow[/tex] w2 as z [tex]\rightarrow[/tex] z0

prove that f(z)/g(z) [tex]\rightarrow[/tex] w1/w2 as z[tex]\rightarrow[/tex] z0

## The Attempt at a Solution

let [tex]\epsilon[/tex] > 0

choose [tex]\delta[/tex] > 0 such that:

|f(z) - w1| < ______ (defined later)

|g(z) - w2| < ______ (defined later)

|f(z)/g(z) - w1/w2| = |f(z)/g(z) - f(z)/w2 + f(z)/w2 - w1/w2|

< |f(z)|*1/|g(z)-w2| + 1/|w2|*|f(z) -w1|

this is where I am stuck, I know that you have to make that add up to epsilon but I'm unsure how to pick them so it works out correctly. Any help would be greatly appreciated.