91Ó°ÊÓ

In Exercises \(5-28\) , find the indefinite integral. $$\int \frac{2 x^{2}+7 x-3}{x-2} d x$$

Evaluating a Limit In Exercises \(15-42\) , evaluate the limit, using L'Hopital's Rule if necessary. $$\lim _{x \rightarrow 5^{-}} \frac{\sqrt{25-x^{2}}}{x-5}$$

In Exercises 13-18, sketch the graph of the function and state its domain. $$f(x)=\ln x-4$$

In Exercises \(15-20\) , sketch the graph of the function. $$y=2^{x^{2}}$$

Using the Horizontal Line Test In Exercises 17-24, use a graphing utility to graph the function. Then use the Horizontal Line Test to determine whether the function is one-to-one on its entire domain and therefore has an inverse function. $$f(x)=1-x^{3}$$

Solving an Exponential or Logarithmic Equation In Exercises \(3-18,\) solve for \(x\) accurate to three decimal places. $$\ln (x-2)^{2}=12$$

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

Using the Horizontal Line Test In Exercises 17-24, use a graphing utility to graph the function. Then use the Horizontal Line Test to determine whether the function is one-to-one on its entire domain and therefore has an inverse function. $$f(\theta)=\sin \theta$$

Evaluating a Limit In Exercises \(15-42\) , evaluate the limit, using L'Hopital's Rule if necessary. $$\lim _{x \rightarrow 0^{+}} \frac{e^{x}-(1+x)}{x^{3}}$$

In Exercises 3-22, find the indefinite integral. $$\int \frac{x-3}{x^{2}+1} d x$$