Consider the quadratic function $f\left(x\right)=-4x^2+32x$. Calculate the slopes of the secant lines between the points $\left(x,f\left(x\right)\right)$ and $\left(4,f\left(4\right)\right)$, for $x=3.5,3.9,3.99,3.999$.

Consider the position function $s(t) = -12t^2 + 60t$. Approximate the instantaneous velocity at $t=1$ by completing the given table with the average velocities.

A runner's position along a track is recorded at various times during a race. The data is presented in a table. Find the runner's average velocity between the time interval of 0 to 2 seconds.

Identify the vertical asymptote of the function $f\left(x\right)=\frac{x^2-4x+4}{2x-8}$.

Determine $\displaystyle \lim_{x \to -2^-}{f(x)}$ using the following graph:

The revenue of a company over time can be modeled by the function $R\left(t\right)=\frac{5000t}{2t+5}$. Determine whether a steady-state exists and provide its value as $t$ approaches $\infty$.

Find the limit of the given function at infinity.

$\lim_{x\to\infty}\left(5+\frac{101}{x^4}\right)$