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. $$ f(x) = x^3 + 3x $$

In Exercises 63-68, use a graphing utility to graph the function and the equations \(y = x\) and \(y = -x\) in the same viewing window. Use the graph to find \( \lim_{x \to 0} f(x) \). \(f(x) = x\ \cos\ x\)

In Exercises 49-68, find the limit by direct substitution. $$ \lim_{x \to 3}\ e^x$$

In Exercises 63-68, use a graphing utility to graph the function and the equations \(y = x\) and \(y = -x\) in the same viewing window. Use the graph to find \( \lim_{x \to 0} f(x) \). \(f(x) = x\ \sin\ \dfrac{1}{x}\)

In Exercises 49-68, find the limit by direct substitution. $$ \lim_{x \to 3}\ \textrm{ln}\ x$$

THINK ABOUT IT Use a graphing utility to graph the function given by \(f(x) = \dfrac{x}{\sqrt{x^2 +1}}\) How many horizontal asymptotes does the function appear to have? What are the horizontal asymptotes?

In Exercises 49-68, find the limit by direct substitution. $$ \lim_{x \to \pi}\ \textrm{sin}\ 2x$$

In Exercises 63-68, use a graphing utility to graph the function and the equations \(y = x\) and \(y = -x\) in the same viewing window. Use the graph to find \( \lim_{x \to 0} f(x) \). \(f(x) = |x|\ \sin\ x\)

In Exercises 65-68, create a scatter plot of the terms of the sequence. Determine whether the sequence converges or diverges. If it converges, estimate its limit. $$a_n = 4\left(\dfrac{2}{3} \right)^n $$

In Exercises 49-68, find the limit by direct substitution. $$ \lim_{x \to \pi}\ \textrm{tan}\ x$$