# Keeping #n# and #T# constant, how do I prove that #P prop 1/V#? What about keeping #n# and #P# constant and showing that #V prop T#?

You can check this just from the ideal gas law.

You can also prove it further:

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For P prop 1/V, use the ideal gas law: PV = nRT. Rearrange to get P prop 1/V. For V prop T, rearrange the ideal gas law as V prop T when n and P are constant.

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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.

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