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This is problem or fifty six of the Stuart Calculus
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eighth edition, section two point three. In the
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theory of relativity, killer ends contraction formula ends.
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Hell equals al subzero. Time is a square root
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. Uh, the quantity one minus b squared over
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C squared This formula expressive the length l of an
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object as a function of its velocity. Be with
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respect in it and observer, where all subzero is
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the length of a dob. Check that rest and
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C is the speed of light. Find the limit
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and be a purchase See from the left with the
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function l ah and interpret the results. Why is
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the last time limit necessary? So let's answer the
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first question first. Well, we see that this
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functional is restricted by this square roots saying which it
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should be clear cannot take any negative numbers. It
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can't be that in mind. The domain of the
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square in here or a quantity inside of this square
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root needs to be, I reckon, greater than
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or equal to zero. This means that one must
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figure than equal to this racial and privately C squared
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needs to be greater than equal to V squared and
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at this point, we see that see must be
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greater than equal to B and in this way has
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via purchasing. We notice Avi is always less than
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thie. So we definitely are approaching C from the
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left. Now find this Lim. We approximate what
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we may be as a week approach. See?
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Well, it's used to excess institution one minus C
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squared over C squared. Excuse us. Screwed of
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one minus one. Which is, of course,
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zero. So the result is that and he doesn't
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want seen. So as your velocity approaches the speed
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of light the length of the object purchase zero.
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This means that the object essentially disappears as you approach
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on the speed of light.