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Calculus
Section 2.5
Section 2.5
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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
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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">
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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.
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