Chapter 1, 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 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 r(x) be the ratio of the perimeters of the two triangles,

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

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

x	4	2	1	0.1	0.01
Perimeter $\Delta$ PAO
Perimeter $\Delta$ PBO
r(x)