1. Limits and Continuity

Determine the end behavior of the following transcendental functions by analyzing appropriate limits. Then provide a simple sketch of the associated graph, showing asymptotes if they exist. 

$f\left(x\right)=\sin x$

Find the limit by creating a table of values.

$\lim_{x\rarr0}-4x+2$

Find the limit by creating a table of values.

$\lim_{x\rarr2}3x^2+5x+1$

Find the limit by creating a table of values.

$\lim_{x\rarr1}\frac{x^2-4}{x-2}$

Find the limit using the graph of $f\left(x\right)$shown.

$\lim_{x\rarr1}f\left(x\right)$

Find the limit using the graph of $f\left(x\right)$shown.

$\lim_{x\rarr-2}f\left(x\right)$

Find the limit using the graph of $f\left(x\right)$shown.

$\lim_{x\rarr4}f\left(x\right)$

Using the graph, find the specified limit or state that the limit does not exist (DNE).

${\lim }_{x\to -2^{-}}f\left(x\right)$, ${\lim }_{x\to -2^{+}}f\left(x\right)$, ${\lim }_{x\to -2^{}}f\left(x\right)$

Using the graph, find the specified limit or state that the limit does not exist (DNE).

$\lim_{x\rightarrow0^{-}}f\left(x\right)$ , $\lim_{x\rightarrow0^{+}}f\left(x\right)$, $\lim_{x\rightarrow0}f\left(x\right)$

Using the graph, find the specified limit or state that the limit does not exist.

$\lim_{x\rightarrow4^{-}}f\left(x\right)$, $\lim_{x\rightarrow4^{+}}f\left(x\right)$, $\lim_{x\rightarrow4}f\left(x\right)$

Find the specified limit or state that the limit does not exist by creating a table of values.

$f\left(x\right)=\frac{1}{x}$

$\lim_{x\rightarrow1^{-}}f\left(x\right)$, $\lim_{x\rightarrow1^{+}}f\left(x\right)$, $\lim_{x\rightarrow1}f\left(x\right)$

Use the graph of $f\left(x\right)$to estimate the value of the limit or state that it does not exist (DNE).

$\lim_{x\rarr1}f\left(x\right)$

Use the graph of $f\left(x\right)$to estimate the value of the limit or state that it does not exist (DNE).

$\lim_{x\rarr-2}f\left(x\right)$

Use the graph of $f\left(x\right)$to estimate the value of the limit or state that it does not exist (DNE).

$\lim_{x\rarr0}f\left(x\right)$

Use the graph of $f\left(x\right)$to estimate the value of the limit or state that it does not exist (DNE).

$\lim_{x\rarr0}f\left(x\right)$