What evidence is there that quasars are small?
The fact that quasars are very luminous and change luminosity over short periods of time means that the must be small.
Massive energy is emitted by quasars across the whole spectrum, with luminosities varying over days, weeks, or months.
The change in luminosity indicates that the energy source must be light days, weeks, or months in size, with a size that is less than the distance light travels during the change in luminosity period.
Supermassive black holes, which are millions to billions of times the mass of the Sun, are the source of quasars. Despite their massive size, supermassive black holes are usually smaller than our solar system.
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Numerous indicators point to quasars being small, such as their high brightness temperatures, quick variability, and connections to comparatively small areas in far-off galaxies.
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The evidence that quasars are small comes from observations of their variability in brightness over short timescales, as well as their high luminosity. Quasars exhibit rapid fluctuations in brightness, suggesting that the emitting region is compact, likely smaller than our solar system. Additionally, the high luminosity of quasars indicates that all this energy is emitted from a very small volume, consistent with a compact central source. This evidence supports the notion that quasars are indeed small objects.
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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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