What caused the 23.5 degrees tilt of earth's axis?
To my knowledge, there is no verified reason that is known, but some theories have been suggested. See the explanation:
Here is one of the leading contenders for an explanation, from Princeton University in 2006:
"By analyzing the magnetic composition of ancient sediments found in the remote Norwegian archipelago of Svalbard, Princeton University's Adam Maloof has lent credence to a 140-year-old theory regarding the way the Earth might restore its own balance if an unequal distribution of weight ever developed in its interior or on its surface.
The theory, known as true polar wander, postulates that if an object of sufficient weight -- such as a supersized volcano -- ever formed far from the equator, the force of the planet's rotation would gradually pull the heavy object away from the axis the Earth spins around. If the volcanoes, land and other masses that exist within the spinning Earth ever became sufficiently imbalanced, the planet would tilt and rotate itself until this extra weight was relocated to a point along the equator."
So, it could be that the tilt is due to the Earth establishing a rotational balance at some point in its early history. Sounds reasonable.
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The tilt of the Earth's axis, approximately 23.5 degrees relative to its orbital plane, is primarily caused by the gravitational interactions between the Earth and the Moon, as well as by the way the Earth formed during its early stages of development.
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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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