How can scientists estimate the size of the universe if it is expanding?
By measuring the red shift of spectral lines.
The red shift of spectral lines (doppler) gives an indication of the expansion of the Universe and can be used to visualize the state of the Universe, (i.e. it's expansion). Red color indicates a longer wavelength and hence expansion.
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By measuring the redshift of light from distant galaxies, monitoring cosmic microwave background radiation, and examining the distribution of galaxies in the universe, scientists can measure the rate at which galaxies are moving away from one another due to the expansion of space. By combining these observations with theoretical models of the universe's expansion, scientists can estimate the universe's size and rate of expansion.
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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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