Difference between revisions of "Nabla derivative at left-scattered"

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(Created page with "==Theorem== If $f$ is continuous at $t$ and $t$ is left-scattered, then $$f^{\nabla}(t) = \dfrac{f(t)-f(\rho(t))}{\nu(t)}.$$ ==Proof== ==References== ...")
 
 
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==Theorem==
 
==Theorem==
If $f$ is continuous at $t$ and $t$ is [[scattered point|left-scattered]], then
+
If $f$ is [[continuity|continuous]] at $t$ and $t$ is [[scattered point|left-scattered]], then
$$f^{\nabla}(t) = \dfrac{f(t)-f(\rho(t))}{\nu(t)}.$$
+
$$f^{\nabla}(t) = \dfrac{f(t)-f(\rho(t))}{\nu(t)},$$
 +
where $f^{\nabla}$ denotes the [[nabla derivative]], $\rho$ denotes the [[backward jump]], and $\nu$ denotes the [[backward graininess]].
  
 
==Proof==
 
==Proof==

Latest revision as of 00:58, 23 August 2016

Theorem

If $f$ is continuous at $t$ and $t$ is left-scattered, then $$f^{\nabla}(t) = \dfrac{f(t)-f(\rho(t))}{\nu(t)},$$ where $f^{\nabla}$ denotes the nabla derivative, $\rho$ denotes the backward jump, and $\nu$ denotes the backward graininess.

Proof

References