Gravitational Force

Calculus
Section 2.5

 

graph:




The function is certainly continuous on r element [0, R) and r element (R,∞).
The only question is whether it is continuous at r = R.
Checking the limit from each side, we find that


R^-)( piecewise | (G M r)/R^3 | r<=R (G M)/r^2 | r>=R) = (G M)/R^2" style="-x-ignore: 1" data-paste-id="1">


R^+)( piecewise | (G M r)/R^3 | r<=R (G M)/r^2 | r>=R) = (G M)/R^2" style="-x-ignore: 1" data-paste-id="2">
Both limits are equal, and the value of F(r) is equal to the limit because of the r ≥ R
clause in the function definition. Therefore the function is continuous for any r > 0.

 

Thanks. Did you try uploading several images? If so, only one image is in display.

 

did you see these imgs

 

Now I can see the images. Thank you.

Note:

It is really humid in NYC. This morning the humidity was 80%. I don't think it has gone down. I do not have an air conditioner in my room. My fan is blowing hot air.

I took two showers today but to no avail. So, in light of this uncomfortable weather condition, I will not do the Intermediate Value Theorem tonight. I will leave it for another day.