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Magazine Problem 8
Find the indefinite integral. $$ \int \frac{x^{2}}{3-x^{3}} d x $$
Problem 11
Sketch the graph of the function and state its domain. $$ f(x)=3 \ln x $$
Problem 13
Use a calculator to approximate the value. Round your answer to two decimal places. \(\arccos (-0.8)\)
Problem 13
Sketch the graph of the function and state its domain. $$ f(x)=\ln 2 x $$
Problem 15
Use a calculator to approximate the value. Round your answer to two decimal places. \(\operatorname{arcsec} 1.269\)
Problem 19
Use a graphing utility to graph the function. Determine whether the function is one-to-one on its entire domain. \(f(x)=\ln x\)
Problem 22
Write the expression in algebraic form. sec (arctan 4x)
Problem 23
In Exercises \(23-28\), use the derivative to determine whether the function is strictly monotonic on its entire domain and therefore has an inverse function. \(f(x)=\ln (x-3)\)
Problem 25
Find the indefinite integral by \(u\) -substitution. (Hint: Let \(u\) be the denominator of the integrand.) $$ \int \frac{1}{1+\sqrt{2 x}} d x $$
Problem 27
Use the derivative to determine whether the function is strictly monotonic on its entire domain and therefore has an inverse function. \(f(x)=2-x-x^{3}\)
