# Math Help - Proving Continuity

1. ## Proving Continuity

Greetings all,

I am not sure which theorem to use to answer this question. It says to not use the Delta/E definition of limit and prove that this function is continuous when x=0. I think the theorem to use is the intermediate value theorem.

the function is g(x)= {x2cos (1/x) when x does not equal 0
and the other is {0 when x=0

2. ## Re: Proving Continuity

Originally Posted by funnybabe
the function is g(x)= {x2cos (1/x) when x does not equal 0
and the other is {0 when x=0
$\left| {x^2 \cos \left( {\frac{1}{x}} \right) - 0} \right| \leqslant \left| {x^2 } \right|$.
Think about $\delta=\sqrt{\varepsilon }$