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**1. Homework Statement**

Give an example of a function f for which the following assertion is false:

If [tex]|f(x)-l|<\epsilon[/tex] when [tex]0<|x-a|<\delta[/tex], then [tex] |f(x)-l|<\epsilon/2[/tex], when [tex] 0<|x-a|<\delta/2[/tex]

**3. The Attempt at a Solution**

I am really not quite sure what I am looking for here. I think i want a function for which [tex]\delta[/tex] gets smaller much more quickly than epsilon does, any input as to what I am actually looking for would be great.