Chapter 1, Problem 2PS

Area Let P(x, y) be a point on the parabola $y=x^2$ in the first quadrant. Consider the triangle $\Delta$

PAO formed by P, A (0, 1), and the origin 0(0, 0), and the triangle $\Delta$

PBO formed by P, B (1, 0). and the origin (see figure).

(a) Write the perimeter of each triangle in terms of x.

(b) Let a(x) be the ratio of the perimeters of the two triangles,

$a(x)=\frac{\text{Area}\Delta PBO}{\text{Area}\Delta PAO}.$

Complete the table. Calculate $\underset{x-0^{+}}{\lim }a(x)$

x	4	2	1	0.1	0.01
Area $\Delta$PAO
Area $\Delta$PBO
a(x)