Finding a Limit Let R be the area of the region in the first quadrant bounded by the parabola and the line , as shown in the figure. Let T be the area of the triangle AOB.
Calculate the limit.
Ā
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The line y=mx+b intersects the parabola in points A and B (see the figure). Find the point P on the arc AOB of the parabola that maximizes the area of the triangle PAB.
Finding a Limit Let T be an equilateral triangle with sides of length 1. Let an be the number of circles that can be packed tightly in n rows inside the triangle. For example, = 1, a2 = 3, and a3 = 6, as shown in the figure. Let An be the combined area of the an circles. Find
Dividing a Region
Let R be the region bounded by the parabola and the -axis (see figure). Find the equation of the line that divides this region into two regions of equal area.
