Consider the quadrilateral #ABCD#, and let #E, N, F, M# be the midpoints of the edges #AB, BC, CD, DA# respectively. How do you prove that #vec(EF)=1/2(vec(AD)+vec(BC))# and #vec(AC)=vec(MN)+vec(EF)#?
Consider the quadrilateral #ABCD# , and let #E, N, F, M# be the midpoints of the edges #AB, BC, CD, DA# respectively. Prove that
#vec(EF)=1/2(vec(AD)+vec(BC))# and #vec(AC)=vec(MN)+vec(EF)#
(From Izu Vaisman's book)
Consider the quadrilateral
(From Izu Vaisman's book)
Please see the proof below.
Apply Chasles' relation
Therefore,
But,
Similarly, using the mid point theorem,
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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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