91Ó°ÊÓ

Verifying Inverse Functions In Exercises \(9-16\) , show that \(f\) and \(g\) are inverse functions(a) analytically and (b) graphically. $$f(x)=3-4 x, \quad g(x)=\frac{3-x}{4}$$

Using Two Methods In Exercises \(7-14\) , evaluate the limit (a) using techniques from Chapters 1 and 3 and (b) using L'Hopital's Rule. $$\lim _{x \rightarrow-1}\left(\frac{1-\sqrt{x+2}}{x+1}\right)$$

Evaluating Inverse Trigonometric Functions In Exercises \(7-14\) , evaluate the expression without using a calculator. $$\arccos (-1)$$

In Exercises \(5-10\) evaluate the expression without using a calculator. $$\log _{27} \frac{1}{9}$$

Solving an Exponential or Logarithmic Equation In Exercises \(3-18,\) solve for \(x\) accurate to three decimal places. $$100 e^{-2 x}=35$$

In Exercises 3-22, find the indefinite integral. $$\int \frac{1}{x \sqrt{x^{4}-4}} d x$$

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

Verifying Inverse Functions In Exercises \(9-16\) , show that \(f\) and \(g\) are inverse functions(a) analytically and (b) graphically. $$f(x)=x^{3}, \quad g(x)=\sqrt[3]{x}$$

In Exercises \(5-28\) , find the indefinite integral. $$\int \frac{4 x^{3}+3}{x^{4}+3 x} d x$$

Using Two Methods In Exercises \(7-14\) , evaluate the limit (a) using techniques from Chapters 1 and 3 and (b) using L'Hopital's Rule. $$\lim _{x \rightarrow 0}\left(\frac{2-2 \cos x}{6 x}\right)$$