$\lim\limits_{x\to -\infty} e^x + 4$

$\lim\limits_{x\to 1} ⁡\dfrac{x − 1}{\ln(x)}$

$\lim\limits_{x\to 0} \dfrac{\cos(2x)}{x}$

$\lim\limits_{x\to 0} ⁡\dfrac{x^2}{|x|}$

For the function below, identify the following limit:

$\lim\limits_{x\to 3} ⁡f(x)$

$f(x) =
\begin{cases}
–x^2 + 7, & x ≤ 3 \\[1ex]
~~~~x − 5, & {x ≥ 3}
\end{cases}$

Identify which of the following functions is increasing at a faster rate on the given domain.

$f(x) = x^2$,        $x ≥ 1$

$g(x) = x$,        $x ≥ 1$

Identify which of the following functions is increasing at a faster rate on the given domain.

$f(x) = x^3 − 3x$,        $2 ≤ x < ∞$

$g(x) = x^3$,        $2 ≤ x < ∞$

$\lim\limits_{x\to \infty} \dfrac{2x^2}{\ln(\sqrt{x})}$

Identify the following limit using the graph below. Note that the graphs $f(x)$ and $g(x)$ are labeled by $f$ and $g$ respectively.

$\lim\limits_{x\to 2} \dfrac{f(x)}{g(x)}$

Identify the following limit using the graph below. Note that the graphs $f(x)$ and $g(x)$ are labeled by $f$ and $g$ respectively.

$\lim\limits_{x\to 3} f(g(x) − 2)$