91Ó°ÊÓ

Finding an Indefinite Integral In Exercises \(1-26,\) find the indefinite integral.. $$ \int \frac{2 x^{2}+7 x-3}{x-2} d x $$

Finding an Indefinite Integral In Exercises \(1-20\) , find the indefinite integral. $$ \int \frac{3}{2 \sqrt{x}(1+x)} d x $$

In Exercises 17–22, find the limit. $$ \lim _{x \rightarrow \infty} \sinh x $$

Sketching a Graph In Exercises \(17-22,\) sketch the graph of the function. $$ y=e^{-x} $$

Finding an Indefinite Integral In Exercises \(1-26,\) find the indefinite integral.. $$ \int \frac{x^{3}-3 x^{2}+5}{x-3} d x $$

Finding an Indefinite Integral In Exercises \(1-20\) , find the indefinite integral. $$ \int \frac{x-3}{x^{2}+1} d x $$

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. \(h(s)=\frac{1}{s-2}-3\)

Using Properties of Logarithms In Exercises 17 and \(18,\) use the properties of logarithms to approximate the indicated logarithms, given that \(\ln 2 \approx 0.6931\) and \(\ln 3 \approx 1.0986\) \(\begin{array}{llll}{\text { (a) } \ln 6} & {\text { (b) } \ln \frac{2}{3}} & {\text { (c) } \ln 81} & {\text { (d) } \ln \sqrt{3}}\end{array}\)

In Exercises 17–22, find the limit. $$ \lim _{x \rightarrow-\infty} \tanh x $$

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. \(g(t)=\frac{1}{\sqrt{t^{2}+1}}\)