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Is there an upper limit to the mass of a star above which it would not enter the AGB? If so, why?

Answer 1

AGB stars have a mass less than about 10 solar masses.

Red giant stars, which form when a star runs out of hydrogen and collapses its core until it reaches a temperature high enough to initiate helium fusion, give rise to AGB stars.

When the hydrogen supply runs out, stars larger than 10 solar masses begin to fuse helium, building up to the point where they have an iron core, which collapses and triggers a supernova explosion.

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Answer 2

Matthew Arnold

The asymptotic giant branch (AGB) phase is not reached by stars with masses higher than about 8 solar masses. Stars that fall below this threshold follow a different evolutionary path, either as a supernova or as a direct collapse into a black hole. This is because stars with higher masses have shorter lifetimes and faster nuclear fusion rates, which keeps them from reaching the AGB phase.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.