Use the following limit definition to determine the slope of the line tangent to the graph of $f$ at $P$, where $f\left(x\right)=\frac{19}{x^3}$ and $P(-1,-19)$:
$m_{\text{tan}}=\underset{x\to a}{\lim }\frac{f\left(x\right)-f\left(a\right)}{x-a}$