91Ó°ÊÓ

1-2. Use a calculator to evaluate, rounding to three decimal places. a. \(e^{2}\) b. \(e^{-2}\) c. \(e^{1 / 2}\)

For each function: a. Find the relative rate of change. b. Evaluate the relative rate of change at the given value(s) of \(t\) $$ f(t)=t^{2}, \quad t=1 \quad \text { and } \quad t=10 $$

Find the derivative of each function. $$ f(x)=x^{2} \ln x $$

Find each logarithm without using a calculator or tables. a. \(\log _{5} 25\) b. \(\log _{3} 81\) c. \(\log _{3} \frac{1}{3}\) d. \(\log _{3} \frac{1}{9}\) e. \(\log _{4} 2\) f. \(\log _{4} \frac{1}{2}\)

For each function: a. Find the relative rate of change. b. Evaluate the relative rate of change at the given value(s) of \(t\) $$ f(t)=t^{3}, t=1 \quad \text { and } \quad t=10 $$

1-2. Use a calculator to evaluate, rounding to three decimal places. a. \(e^{3}\) b. \(e^{-3}\) c. \(e^{1 / 3}\)

Find the derivative of each function. $$ f(x)=\frac{\ln x}{x^{3}} $$

Find each logarithm without using a calculator or tables. a. \(\log _{3} 27\) b. \(\log _{2} 16\) c. \(\log _{16} 4\) d. \(\log _{4} \frac{1}{4}\) e. \(\log _{2} \frac{1}{8}\) f. \(\log _{9} \frac{1}{3}\)

Find each logarithm without using a calculator or tables. a. \(\ln \left(e^{10}\right)\) b. \(\ln \sqrt{e}\) c. \(\ln \sqrt[3]{e^{4}}\) d. \(\ln 1\) e. \(\ln \left(\ln \left(e^{e}\right)\right) \quad\) f. \(\ln \left(\frac{1}{e^{3}}\right)\)

For each function: a. Find the relative rate of change. b. Evaluate the relative rate of change at the given value(s) of \(t\) $$ f(t)=100 e^{0.2 t}, \quad t=5 $$