In Class Practice $2$

The problems below are meant to give some additional practice with topics we've worked on in class over the last few days.

Feel free to work with those around you and ask me any questions.

Turn in your solutions and work on a separate piece of paper at the end of class $($make sure to put your name on it$!)$

Find a value of $c$ that makes the following function continuous at all real numbers: values of

$f(x)=\{\begin{array}{ccc}cx+6& if& x2\\ (x+1{)}^2+c& if& x>2\end{array}$

For what values of $x$ is the following function not continuous? For each point, determine if the graph has a hole, vertical asymptote, or neither.

$g(x)=\frac{x^2+5x+4}{x^2-2x-3}$

Sketch a graph of a function $f(x)$ that satisfies all of the following conditions:

$\underset{x{0}^{-}}{lim}f(x)=-2,\underset{x{0}^{+}}{lim}f(x)=1,f(0)=3$

Find the equation of the tangent line to the graph of $f(x)=\frac{1}{x}$ at $x=2.$

Use the limit definition of the derivative to compute $g^{\text{'}}(x)$ for $g(x)=2x^2-4x+3$

$[$Challenge$/$Extra Credit$]$ Find an example of two functions $f(x)$ and $g(x)$ such that $\underset{x0}{lim}f(x)$ and $\underset{x0}{lim}g(x)$ don't exist, but $\underset{x0}{lim}(f+g)(x)$ does exist.