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## Homework Statement

Let |f(x)|≤g(x) for all x∈ M

_{f}∩M

_{g}.

What is lim

_{x-->0}f(x) when lim

_{ x-->0}g(x)=0?

What is lim

_{x-->0}f(x) when lim

_{ x-->0}g(x)=3?

## The Attempt at a Solution

Well, given that|f(x)|≤g(x), lim

_{ x-->0}g(x)=0 intuitively implies to me that | lim

_{x-->0}f(x) |≤0

therefore | lim

_{x-->0}f(x) |=0 --> lim

_{x-->0}f(x)=0

AND when lim

_{ x-->0}g(x)=3

|lim

_{x-->0}f(x)|≤3 ⇔ -3 ≤lim

_{x-->0}f(x)≤3

Is my reasoning correct?