Search

6.3: Комплексна диференціація
https://ukrayinska.libretexts.org/%D0%9C%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B0/%D0%9B%D1%96%D0%BD%D1%96%D0%B9%D0%BD%D0%B0_%D0%B0%D0%BB%D0%B3%D0%B5%D0%B1%D1%80%D0%B0/%D0%9A%D0%BD%D0%B8%D0%B3%D0%B0%3A_%D0%9C%D0%B0%D1%82%D1%80%D0%B8%D1%87%D0%BD%D0%B8%D0%B9_%D0%B0%D0%BD%D0%B0%D0%BB%D1%96%D0%B7_(Cox)/06%3A_%D0%9A%D0%BE%D0%BC%D0%BF%D0%BB%D0%B5%D0%BA%D1%81%D0%BD%D0%B8%D0%B9_%D0%B0%D0%BD%D0%B0%D0%BB%D1%96%D0%B7_I/6.03%3A_%D0%9A%D0%BE%D0%BC%D0%BF%D0%BB%D0%B5%D0%BA%D1%81%D0%BD%D0%B0_%D0%B4%D0%B8%D1%84%D0%B5%D1%80%D0%B5%D0%BD%D1%86%D1%96%D0%B0%D1%86%D1%96%D1%8F
$\begin{align*} \lim z \rightarrow z_{0} \frac{z^2-z_{0}^2}{z-z_{0}} &= \lim_{z \rightarrow z_{0}} \frac{(z-z_{0})(z+z_{0})}{z-z_{0}} \\[4pt] &= 2z_{0} \end{align*}$ \[\begin{align*} \lim z \rightar... $\begin{align*} \lim z \rightarrow z_{0} \frac{z^2-z_{0}^2}{z-z_{0}} &= \lim_{z \rightarrow z_{0}} \frac{(z-z_{0})(z+z_{0})}{z-z_{0}} \\[4pt] &= 2z_{0} \end{align*}$ $\begin{align*} \lim z \rightarrow z_{0} \frac{e^{z}-e^{z_{0}}}{z-z_{0}} &= e^{z_{0}} \lim_{z \rightarrow z_{0}} \frac{e^{z-z_{0}}-1}{z-z_{0}} \\[4pt] &= e^{z_{0}} \lim_{z \rightarrow z_{0}} \sum_{n = 0}^{\infty} \frac{(z-z_{0})^{n}}{(n+1)!} \\[4pt] &= e^{z_{0}} \end{align*}$