91Ó°ÊÓ

In Exercises 59-62, find the derivative of \(f\). Use the derivative to determine any points on the graph of \(f\) at which the tangent line is horizontal. Use a graphing utility to verify your results. $$ f(x) = x^2 - 6x +4 $$

In Exercises 49-68, find the limit by direct substitution. $$ \lim_{x \to 3}\ \sqrt[3]{x^2-1}$$

In Exercises 55-62, graph the function. Determine the limit (if it exists) by evaluating the corresponding one-sided limits. \\[ \lim_{x \to 1} f(x)\ \textrm{where}\ f(x) = \begin{cases} 2x+1, & \quad x<1\\\ 4-x^2, & \quad x\geq1 \end{cases} \\]

TRUE OR FALSE? In Exercises 59-62, determine whether the statement is true or false. Justify your answer. If a sequence converges, then it has a limit.

In Exercises 55-62, graph the function. Determine the limit (if it exists) by evaluating the corresponding one-sided limits. \\[ \lim_{x \to 1} f(x)\ \textrm{where}\ f(x) = \begin{cases} 4-x^2, & \quad x\leq1\\\ 3-x, & \quad x>1 \end{cases} \\]

In Exercises 49-68, find the limit by direct substitution. $$ \lim_{x \to 7}\ \dfrac{5x}{\sqrt{x+2}}$$

In Exercises 59-62, find the derivative of \(f\). Use the derivative to determine any points on the graph of \(f\) at which the tangent line is horizontal. Use a graphing utility to verify your results. $$ f(x) = 3x^3 - 9x $$

In Exercises 55-62, graph the function. Determine the limit (if it exists) by evaluating the corresponding one-sided limits. \\[ \lim_{x \to 0} f(x)\ \textrm{where}\ f(x) = \begin{cases} 4-x^2, & \quad x\leq0\\\ x+4, & \quad x>0 \end{cases} \\]

In Exercises 49-68, find the limit by direct substitution. $$ \lim_{x \to 8}\ \dfrac{\sqrt{x+1}}{x-4}$$

TRUE OR FALSE? In Exercises 59-62, determine whether the statement is true or false. Justify your answer. When the degrees of the numerator and denominator of a rational function are equal, the limit does not exist.