# Calculus homework #2 due 2-16

1. Does $\lim_{x\rightarrow 1}\cot(\pi x)$ exist? Explain your answer.
2. Consider the graph of $f(x)$

State the value of each quantity, if it exists. If it does not exist, explain why.

$\lim_{x\rightarrow 0}f(x)$    $\lim_{x\rightarrow 0^{+}}f(x)$    $\lim_{x\rightarrow 2^{-}}f(x)$    $f(2)$    $\lim_{x\rightarrow 2}f(x)$

3. Sketch the graph of an example of a function $f(x)$ such that $\lim_{x\rightarrow 2}f(x)=3$, $\lim_{x\rightarrow -2}f(x)=0$, and $f(2)=f(-2)=1$.

4. Sketch the graph of an example of a function $f(x)$ such that $\lim_{x\rightarrow -1^{-}}f(x)=4$, $\lim_{x\rightarrow 1^{-}}f(x)=2$, and $f(x)$ is even.