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Chapter 8: Problem 20
Find the indefinite integral. $$ \int \sec \frac{x}{2} d x $$
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Seasonal Sales The monthly sales (in millions of units) of snow blowers can be modeled by \(S=15+6 \sin \frac{\pi(t-8)}{6}, \quad 0 \leq t \leq 12\) where \(t\) is the time in months, with \(t=1\) corresponding to January. Find the average monthly sales $$ \begin{array}{l}{\text { (a) during a year. }} \\ {\text { (b) from July through December. }}\end{array} $$
complete the table (using a spreadsheet or a graphing utility set in radian mode) to estimate \(\lim _{x \rightarrow 0} f(x)\). $$ \begin{array}{|c|c|c|c|c|c|c|}\hline x & {-0.1} & {-0.01} & {-0.001} & {0.001} & {0.01} & {0.1} \\ \hline f(x) & {} & {} & {} & {} \\ \hline\end{array} $$ $$ f(x)=\frac{\sin 2 x}{\sin 3 x} $$
complete the table (using a spreadsheet or a graphing utility set in radian mode) to estimate \(\lim _{x \rightarrow 0} f(x)\). $$ \begin{array}{|c|c|c|c|c|c|c|}\hline x & {-0.1} & {-0.01} & {-0.001} & {0.001} & {0.01} & {0.1} \\ \hline f(x) & {} & {} & {} & {} \\ \hline\end{array} $$ $$ f(x)=\frac{\tan 2 x}{x} $$
find the period and amplitude. $$ y=-2 \sin 10 x $$
The number \(W(\) in thousands) of construction workers employed in the United States during 2006 can be modeled by \(W=7594+455.2 \sin (0.41 t-1.713)\) where \(t\) is the time in months, with \(t=1\) corresponding to January \(1 .\) (a) Use a graphing utility to graph \(W\) (b) Did the number of construction workers exceed 8 million in \(2006 ?\) If so, during which month(s)?
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