Difference between revisions of "Delta derivative at right-dense"

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(Created page with "==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 derivative|delta differen...")
 
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==References==
 
==References==
* {{BookReference|Dynamic Equations on Time Scales|2001|Martin Bohner|author2=Allan Peterson|prev=Delta derivative at right-scattered|next=Simple useful formula}}: Theorem 1.16
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* {{BookReference|Dynamic Equations on Time Scales|2001|Martin Bohner|author2=Allan Peterson|prev=Delta derivative at right-scattered|next=Simple useful formula}}: Theorem 1.16 (iii)

Revision as of 05:24, 10 June 2016

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