91Ó°ÊÓ

Show that \(f\) and \(g\) are inverse functions (a) analytically and (b) graphically. \(f(x)=5 x+1, \quad g(x)=\frac{x-1}{5}\)

Finding an Indefinite Integral In Exercises \(1-26,\) find the indefinite integral.. $$ \int \frac{5}{x} d x $$

In Exercises 1–6, evaluate the function. If the value is not a rational number, round your answer to three decimal places. $$ \begin{array}{l}{\text { (a) } \sinh 3} \\ {\text { (b) } \tanh (-2)}\end{array} $$

Evaluating a Logarithm In Exercises \(1-4,\) use a graphing utility to evaluate the logarithm by (a) using the natural logarithm key and (b) using the integration capabilities to evaluate the integral \(\int_{1}^{x}(1 / t) d t .\) $$ \ln 45 $$

Evaluating a Logarithmic Expression In Exercises \(1-4\) , evaluate the expression without using a calculator. $$ \log _{2} \frac{1}{8} $$

Solving an Exponential or Logarithmic Equation In Exercises 1-16, solve for \(x\) accurate to three decimal places. $$ e^{\ln x}=4 $$

Finding an Indefinite Integral In Exercises \(1-20\) , find the indefinite integral. $$ \int \frac{d x}{\sqrt{9-x^{2}}} $$

Evaluating a Logarithm In Exercises \(1-4,\) use a graphing utility to evaluate the logarithm by (a) using the natural logarithm key and (b) using the integration capabilities to evaluate the integral \(\int_{1}^{x}(1 / t) d t .\) $$ \ln 8.3 $$

Solving an Exponential or Logarithmic Equation In Exercises 1-16, solve for \(x\) accurate to three decimal places. $$ e^{\ln 3 x}=24 $$

Finding an Indefinite Integral In Exercises \(1-26,\) find the indefinite integral.. $$ \int \frac{10}{x} d x $$