2.3 Limit laws; Question 130

[Eigenvalue]

The density of an object is given by its mass divided by its volume p=[tex]\frac{m}{V}[/tex]

a) Use a calculator to plot the volume as a function of density, assuming that you are examining an object with mass 8kg (m=8)

b) Evaluate [tex]\lim_{x \to 0+}V(p)[/tex] and explain the physical meaning

[Eigenvalue]

a) Use a calculator to plot the volume as a function of density, assuming that you are examining an object with mass 8kg (m=8)

p=[tex]\frac{m}{V}[/tex]
V=[tex]\frac{m}{p}[/tex]
Let m=8
V(p)=[tex]\frac{8}{p}[/tex]
see attachment for the graph

Note: I added a version of the graph with a slope field; if the slope field is inaccurately drawn, please correct it.


b) Evaluate [tex]\lim_{x \to 0+}V(p)[/tex] and explain the physical meaning
[tex]\lim_{x \to 0+}V(p)[/tex]=[tex]\lim_{x \to 0+} \infty[/tex]

As the volume of the object increases, approaching infinity, the density of the object decreases, approaching 0.