91Ó°ÊÓ

Using a Right Triangle In Exercises \(19-24\) , use the figure to write the expression in algebraic form given \(y=\arccos x,\) where \(0

In Exercises \(21-30,\) use the properties of logarithms to expand the logarithmic expression. $$\ln (x y z)$$

In Exercises 23-34, evaluate the definite integral. $$\int_{0}^{\sqrt{3} / 2} \frac{1}{1+4 x^{2}} d x$$

In Exercises \(21-30,\) use the properties of logarithms to expand the logarithmic expression. $$\ln \left(x \sqrt{x^{2}+5}\right)$$

Determining Whether a Function Has an Inverse Function In Exercises 25-30, use the derivative to determine whether the function is strictly monotonic on its entire domain and therefore has an inverse function. $$f(x)=2-x-x^{3}$$

In Exercises \(5-28\) , find the indefinite integral. $$\int \frac{1}{\sqrt{x}(1-3 \sqrt{x})} d x$$

Evaluating a Limit In Exercises \(15-42\) , evaluate the limit, using L'Hopital's Rule if necessary. $$\lim _{x \rightarrow \infty} \frac{7 x^{3}-2 x+1}{6 x^{3}+1}$$

Evaluating an Expression In Exercises \(25-28\) , evaluate each expression without using a calculator. (Hint: Sketch a right triangle, as demonstrated in Example 3.) (a) \(\sin \left(\arctan \frac{3}{4}\right)\) (b) \(\sec \left(\arcsin \frac{4}{5}\right)\)

In Exercises \(21-26,\) solve for \(x\) (a) \(x^{2}-x=\log _{5} 25\) (b) \(3 x+5=\log _{2} 64\)

Evaluating an Expression In Exercises \(25-28\) , evaluate each expression without using a calculator. (Hint: Sketch a right triangle, as demonstrated in Example 3.) (a) \(\tan \left(\arccos \frac{\sqrt{2}}{2}\right)\) (b) \(\cos \left(\arcsin \frac{5}{13}\right)\)