Using polar coordinates, parametrize the region R enclosed b…

Using polar coordinates, parametrize the region R enclosed by the circle \(x^2+y^2=1\). Then find the volume under the surface \(f(x,y)=1-x^2-y^2\) over the region R.  (Hint: \(\displaystyle \int\int_R f(x,y) \;dxdy = \int\int_R f(r,\theta) \;r\;drd\theta\) )    

You arrive at a National Park and are given a contour map. Y…

You arrive at a National Park and are given a contour map. You’re told that if you hike in a straight line on this map from your current location of \((-2, -1)\) to the point \((4,2)\), you will encounter some beautiful views. Before you set out, you learn that the function \(f(x,y) = xy + y^2\) describes the elevation (in hundreds of feet) in your area. Calculate the absolute maximum and minimum elevations along your hiking trail.