Delta derivative at right-dense

From timescalewiki
Revision as of 15:19, 21 January 2023 by Tom (talk | contribs)
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)
Jump to: navigation, search

Theorem

Let $\mathbb{T}$ be a time scale, $t \in \mathbb{T}$ be right-dense. Then $f \colon \mathbb{T} \rightarrow \mathbb{R}$ is delta differentiable at $t$ if and only if the limit $$f^{\Delta}(t)=\displaystyle\lim_{s \rightarrow t} \dfrac{f(t)-f(s)}{t-s}$$ exists.

Proof

References