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Chapter 13: Problem 6
Find the intercepts and sketch the graph of the plane. $$ 2 x-y+z=4 $$
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The revenues \(y\) (in millions of dollars) for Earthlink from 2000 through 2006 are shown in the table. $$ \begin{aligned} &\begin{array}{|l|l|l|l|l|} \hline \text { Year } & 2000 & 2001 & 2002 & 2003 \\ \hline \text { Revenue, } y & 986.6 & 1244.9 & 1357.4 & 1401.9 \\ \hline \end{array}\\\ &\begin{array}{|l|l|l|l|} \hline \text { Year } & 2004 & 2005 & 2006 \\ \hline \text { Revenue, } y & 1382.2 & 1290.1 & 1301.3 \\ \hline \end{array} \end{aligned} $$ (a) Use a graphing utility or a spreadsheet to create a scatter plot of the data. Let \(t=0\) represent the year 2000 . (b) Use the regression capabilities of a graphing utility or a spreadsheet to find an appropriate model for the data. (c) Explain why you chose the type of model that you created in part (b).
Exercises 55 and 56, determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false. $$ \int_{2}^{5} \int_{1}^{6} x d y d x=\int_{1}^{6} \int_{2}^{5} x d x d y $$
Find the average value of \(f(x, y)\) over the region \(R\). $$ \begin{aligned} &f(x, y)=x^{2}+y^{2}\\\ &R: \text { square with vertices }(0,0),(2,0),(2,2),(0,2) \end{aligned} $$
Evaluate the partial integral. $$ \int_{1}^{e} \frac{y \ln x}{x} d x $$
Set up the integral for both orders of integration and use the more convenient order to evaluate the integral over the region \(R\). $$ \begin{aligned} &\int_{R} \int \frac{y}{1+x^{2}} d A\\\ &R: \text { region bounded by } y=0, y=\sqrt{x}, x=4 \end{aligned} $$
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