Let a ∈ R {\displaystyle {}a\in \mathbb {R} } and let
be continuous functions with
Show that there exists some δ > 0 {\displaystyle {}\delta >0} such that
holds for all x ∈ [ a − δ , a + δ ] {\displaystyle {}x\in [a-\delta ,a+\delta ]} .
and let
such that
![{\displaystyle {}x\in [a-\delta ,a+\delta ]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/6c9b3bafaa2faac72bc38dad249dc53053ba0cb2)
.
