Exam 2: Derivatives

For what value of the constant c is the function f continuous on $(-\infty, \infty) ?$ $f(x)=\left\{\begin{array}{lll}c x+7 & \text { for } & x \leq 2 \\c x^{2}-5 & \text { for } & x>2\end{array}\right.$

Evaluate the limit. $\lim _{x \rightarrow-9}|x+9|$

Find the limit. $\lim _{x \rightarrow-\infty} \frac{\sqrt{x^{2}-49}}{2 x-6}$

The symbol $\lfloor\rfloor$ can be used to denote the greatest integer function, which is defined by $\lfloor x\rfloor=$ the greatest integer n such that $n \leq x \text {. }$ Use the graph of the function to find the indicated limit, if it exists. $\lim _{x \rightarrow 0.7}\lfloor x\rfloor$