91Ó°ÊÓ

Evaluating a Limit In Exercises \(11-42,\) evaluate the limit, using L'Hopital's Rule if necessary. $$ \lim _{x \rightarrow 0} \frac{\sin a x}{\sin b x}, \text { where } a, b \neq 0 $$

Using Partial Fractions In Exercises \(5-22,\) use partial fractions to find the indefinite integral. $$ \int \frac{x}{16 x^{4}-1} d x $$

Finding an Indefinite Integral Involving Secant and Tangent In Exercises \(19-32,\) find the indefinite integral. $$ \int \sec ^{4} 2 x d x $$

Using Formulas In Exercises \(17-20,\) use the Special Integration Formulas (Theorem 8.2 ) to find the indefinite integral. $$ \int \sqrt{5 x^{2}-1} d x $$

Use integration tables to find the indefinite integral. \(\int \frac{1}{x^{2}+4 x+8} d x\)

Finding an Indefinite Integral In Exercises \(21-36,\) find the indefinite integral. $$ \int \frac{1}{\sqrt{16-x^{2}}} d x $$

In Exercises 11–30, find the indefinite integral. (Note: Solve by the simplest method—not all require integration by parts.) $$ \int x \sqrt{x-5} d x $$

Finding an Indefinite Integral Involving Secant and Tangent In Exercises \(19-32,\) find the indefinite integral. $$ \int \sec ^{3} \pi x d x $$

Using Partial Fractions In Exercises \(5-22,\) use partial fractions to find the indefinite integral. $$ \int \frac{x^{2}+5}{x^{3}-x^{2}+x+3} d x $$

Evaluating a Limit In Exercises \(11-42,\) evaluate the limit, using L'Hopital's Rule if necessary. $$ \lim _{x \rightarrow 0} \frac{\arcsin x}{x} $$