I have this one problem in my Calculus 1 assignment that I'd like to ask.
The gravitational force exerted by the planet Earth on a unit mass at a distance $r$ from the center of the planet is
$$F(r) = \begin{cases} \frac{GMr}{R^3} & r < R \\ \frac{GM}{r^2} & r \ge R \end{cases}$$
where $M$ is the mass of Earth, $R$ is its radius, and $G$ is the gravitational constant. Is $F$ a
continuous function of $r$?
I have no idea where to start and I'm completely stuck here.
Best Answer
Hint: Since both pieces of the piecewise function are continuous functions in their respective domains of definition, it is just required that the continuity be checked at the point $r=R$, which would be done by checking for the following conditions: