Chapter 2, Problem 1PS

Perimeter 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 O (0, 0), and the triangle $\Delta PBO$ formed by P, B (1, 0), and the origin (see figure).

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

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

$r\left(x\right)=\frac{\text{Perimeter }\Delta PAO}{\text{Perimeter }\Delta PBO}\cdot$

Complete the table. Calculate $\underset{x\to 0^{+}}{\lim }r\left(x\right)$.

x 4210.1 0.01

Perimeters $\Delta PAO$

Perimeters $\Delta PBO$

r(x)