91Ó°ÊÓ

In Exercises 23-34, evaluate the definite integral. $$\int_{\sqrt{3}}^{3} \frac{1}{x \sqrt{4 x^{2}-9}} d x$$

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) \(\cos \left(\arcsin \frac{5}{13}\right)\)

Evaluating a Limit In Exercises \(15-42\) , evaluate the limit, using L'Hopital's Rule if necessary. $$\lim _{x \rightarrow \infty} \frac{8-x}{x^{3}}$$

In Exercises \(5-28\) , find the indefinite integral. $$\int \frac{1}{x^{2 / 3}\left(1+x^{1 / 3}\right)} d x$$

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. $$f(x)=x^{3}-6 x^{2}+12 x$$

In Exercises 23-34, evaluate the definite integral. $$\int_{1}^{7} \frac{1}{9+(x+2)^{2}} d x$$

Evaluating a Limit In Exercises \(15-42\) , evaluate the limit, using L'Hopital's Rule if necessary. $$\lim _{x \rightarrow \infty} \frac{x^{2}+4 x+7}{x-6}$$

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. $$f(x)=8 x^{3}+x^{2}-1$$

Evaluating an Expression In Exercises \(25-28\) , evaluate each expression without using a calculator. (Hint: Sketch a right triangle, as demonstrated in Example 3.) \((a) \cot \left[\arcsin \left(-\frac{1}{2}\right)\right]\) \((b) \csc \left[\arctan \left(-\frac{5}{12}\right)\right]\)

In Exercises \(5-28\) , find the indefinite integral. $$\int \frac{6 x}{(x-5)^{2}} d x$$