Chapter 13: Problem 25
Find the critical points and test for relative extrema. List the critical points for which the Second-Partials Test fails. $$ f(x, y)=(x y)^{2} $$
Chapter 13: Problem 25
Find the critical points and test for relative extrema. List the critical points for which the Second-Partials Test fails. $$ f(x, y)=(x y)^{2} $$
All the tools & learning materials you need for study success - in one app.
Get started for freeSet up the integral for both orders of integration and use the more convenient order to evaluate the integral over the region \(R\). $$ \begin{aligned} &\int_{R} \int x d A\\\ &R: \text { semicircle bounded by } y=\sqrt{25-x^{2}} \text { and } y=0 \end{aligned} $$
Use a symbolic integration utility to evaluate the double integral. $$ \int_{0}^{2} \int_{x^{2}}^{2 x}\left(x^{3}+3 y^{2}\right) d y d x $$
Evaluate the partial integral. $$ \int_{1}^{2 y} \frac{y}{x} d x $$
Use the regression capabilities of a graphing utility or a spreadsheet to find the least squares regression quadratic for the given points. Then plot the points and graph the least squares regression quadratic. $$ (0,0),(2,2),(3,6),(4,12) $$
Use a double integral to find the volume of the solid bounded by the graphs of the equations. $$ z=x^{2}, z=0, x=0, x=2, y=0, y=4 $$
What do you think about this solution?
We value your feedback to improve our textbook solutions.