Difference between revisions of "Delta derivative at right-dense"
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| − | * {{BookReference|Dynamic Equations on Time Scales|2001|Martin Bohner|author2=Allan Peterson|prev=Delta derivative at right-scattered|next= | + | * {{BookReference|Dynamic Equations on Time Scales|2001|Martin Bohner|author2=Allan Peterson|prev=Delta derivative at right-scattered|next=Delta simple useful formula}}: Theorem 1.16 (iii) |
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Latest revision as of 15:19, 21 January 2023
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
- Martin Bohner and Allan Peterson: Dynamic Equations on Time Scales (2001)... (previous)... (next): Theorem 1.16 (iii)
