Chapter 2.1, Problem 1QCE

The slope $m_{\tan }$ of the tangent line to the curve $y=f\left(x\right)$ at the point $P\left(x_0,f\left(x_0\right)\right)$ is given by

$m_{\tan }=\underset{x\to x_0}{\lim }\text{\_\_\_\_\_\_\_}=\underset{h\to 0}{\lim }\text{\_\_\_\_\_\_\_}$