Does the space taken up by matter also expand as the universe expands?
No! Any region in space that is denser than a a certain critical value will decouple itself from expansion and will not expand anymore. Detailed explanation is given below.
In 1971, Gunn and Gott conducted a thorough analysis of the problem of what happens to mass distributions in an expanding universe under the ideal scenario of a spherical matter distribution in a flat, matter-dominated expanding universe, known as the Einstein-deSitter Universe.
Reference: Gunn, James E.; Gott, J. Richard, III Title: On the Infall of Matter Into Clusters of Galaxies and Some Effects on Their Evolution Publication: Astrophysical Journal, vol. 176, p.1
A summary of their conclusion states that while there won't be a gravitational collapse if matter is distributed uniformly throughout the universe, expansion will eventually cause a dilution of density.
In an expanding universe, gravity is not the only force at work; caught in the background expansion, these over-dense regions expand slowly compared to the surrounding under-dense regions. If the matter is distributed non-uniformly in a static universe, then the over-dense regions will become denser assisted by gravitation.
Structures like galaxies and local groups of galaxies are stable and do not expand anymore; however, some massive galaxy clusters may still be expanding but eventually turn around and collapse, while the rest of the Universe expands. This is how structures like galaxies, galaxy clusters, etc. form. Once a system collapses in this way, it totally decouples itself from the expansion and will not participate in it anymore.
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No, the space that matter takes up does not expand with the universe. But, as the universe expands, so does the distance between objects and galaxies, but the matter inside those objects and galaxies stays the same.
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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.
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.
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.
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.

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