Chapter 1: Problem 53
Use the properties of logarithms to expand the logarithmic expression. $$ \ln \frac{2}{3} $$
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If the functions \(f\) and \(g\) are continuous for all real \(x\), is \(f+g\) always continuous for all real \(x ?\) Is \(f / g\) always continuous for all real \(x ?\) If either is not continuous, give an example to verify your conclusion.
In Exercises 115 and \(116,\) find the point of intersection of the graphs of the functions. $$ \begin{array}{l} y=\arccos x \\ y=\arctan x \end{array} $$
In Exercises \(131-134,\) sketch the graph of the function. Use a graphing utility to verify your graph. $$ f(x)=\arcsin (x-1) $$
Prove that if a function has an inverse function, then the inverse function is unique.
Use a graphing utility to graph \(f(x)=\sin x \quad\) and \(\quad g(x)=\arcsin (\sin x)\) Why isn't the graph of \(g\) the line \(y=x ?\)
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