Could the big bang have started with a black hole exploding?
Yes.
The answer, however, could just as easily be no. The truth is that we do not know what existed even a single second before the big bang; at this point, the best theory is that there once was a singularity that contained everything that is currently visible in the universe in a form so compressed that it may have been as small as a grapefruit.
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No, a black hole didn't explode to cause the Big Bang; rather, according to the Big Bang theory, the universe started out as a singularity, or point of infinite density, about 13.8 billion years ago, and it expanded rapidly in an event known as the Big Bang, which led to the formation of the universe as we know it today. Black holes can occur when massive stars collapse, but they are not the cause of the Big Bang.
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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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