# 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=Simple useful formula}}: Theorem 1.16 | + | * {{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

- Martin Bohner and Allan Peterson:
*Dynamic Equations on Time Scales*(2001)... (previous)... (next): Theorem 1.16 (iii)