Chapter 1.4, Problem 34E

To determine

To explain: the increment of c.

Answer to Problem 34E

The width of the graph of the family of curves will increase as $c$ increases.

Explanation of Solution

Given information:

The curves with equations

  $y=\frac{|x|}{\sqrt{c-x^2}}$

Calculation:

The sketch of the curves represented by this equation, for $c=1,2,3,4,10$ is shown below:

  

From the figure, we observe that the curves of the family $y=\frac{|x|}{\sqrt{c-x^2}}$ will form the shape of the nose of a bullet, so that this family of curves is called as bullet-nose curves.

As the value of $c$ increases from $1to10$ , the wideness of the graph will increase.

Hence, we can conclude that, the width of the graph of the family of curves will increase as $c$ increases.