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Difference Quotient


\begin{displaymath}
\Delta_h f(x) \equiv {f(x+h)-f(x)\over h} = {\Delta f\over h}.
\end{displaymath}

It gives the slope of the Secant Line passing through $f(x)$ and $f(x+h)$. In the limit $n\to 0$, the difference quotient becomes the Partial Derivative

\begin{displaymath}
\lim_{h\to 0} \Delta_{x(h)} f(x, y)={\partial f\over\partial x}.
\end{displaymath}




© 1996-9 Eric W. Weisstein
1999-05-24