Let [math] be the function given by [math]. We will investigate the behavior of both the numerator and denominator of [math] near the point where [math]. Let [math] and [math]. Find the local linearizations of [math] and [math] at [math], and call these functions [math] and [math], respectively.
[math]
[math]

Explain why [math] for [math] near [math].

Evaluate the limit:
[math]

Use your work to make an educated guess about [math].
[math]

You could confirm your educated guess by inspecting the graph of [math].