Is the observable universe is the same size today as it was a few million years ago?
No
Keep in mind the word "observable" means what we could in theory see, that is things that were close enough from light to have left those locations and arrived at the Earth. Since the universe is 13.8 billion years old (aprox) then theoretically only things within 13.8 billion light years would be close enough for us to "see" them. That means that a few million years ago the observable universe was a few million light years smaller.
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Certainly, the observable universe has expanded over time due to the Big Bang, which caused galaxies to move apart. As a result, the observable universe is not the same size as it was a few million years ago.
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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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