Chapter 4, Problem 62RE

As shown in the accompanying figure on the next page, suppose that a boat enters the river at the point $\left(1,0\right)$ and maintains a heading toward the origin. As a result of the strong current, the boat follows the path $y=\frac{x^{10/3}-1}{2x^{2/3}}$ where $x$ and $y$ are in miles.

(a) Graph the path taken by the boat.

(b) Can the boat reach the origin? If not, discuss its fate and find how close it comes to the origin.