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4th Edition

James Stewart

Publisher: Cengage Learning

ISBN: 9781337687805

Chapter 2, Problem 10P

**(a)**

To determine

**To find:** The position of the point *P* in the given process and to check whether *P* have a limiting position.

Expert Solution

The limiting position is

**Graph:**

**Calculation:**

Let the coordinate system and drop a perpendicular from *P.*

From the triangle

And from the triangle

By using double-integral formula for tangents,

Simplifying above equation

Applying cross multiplication

As the altitude *AM* decreases in length, the point *P* will approach the *x*-axis, means *y* approaches to 0. So the limiting location of *P* exists and it must be one of the root of the equation. The point *P* can never be to the left of the altitude *AM*, so here *x* not equal to zero, so it must be

Thus, the limiting position is

**(b)**

To determine

**To find:** The equation of the curve and sketch the path traced out by *P.*

Expert Solution

The *P* only traces out the part of the curve with

**Graph:**

**Calculation:**

Take the equation (1) from the part (a) *P.*

As *x* approach 1,

*y* approach 1.

Thus, *P* only traces out the part of the curve with