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In the theory of relativity, the Lorentz contraction formula $$ L = L_0 \sqrt{1 - v^2/c^2} $$expresses the length $ L $ of an object as a function of its velocity $ v $ with respect to an observer, where $ L_0 $ is the length of the object at rest and $ c $ is the speed of light. Find $ \displaystyle \lim_{v \to c}-L $ and interpret the result. Why is a left-hand limit necessary?
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Calculus 1 / AB
Chapter 2
Limits and Derivatives
Section 3
Calculating Limits Using the Limit Laws
Limits
Derivatives
Missouri State University
Harvey Mudd College
University of Michigan - Ann Arbor
Idaho State University
Lectures
04:40
In mathematics, the limit of a function is the value that the function gets very close to as the input approaches some value. Thus, it is referred to as the function value or output value.
In mathematics, a derivative is a measure of how a function changes as its input changes. Loosely speaking, a derivative can be thought of as how much one quantity is changing in response to changes in some other quantity; for example, the derivative of the position of a moving object with respect to time is the object's velocity. The concept of a derivative developed as a way to measure the steepness of a curve; the concept was ultimately generalized and now "derivative" is often used to refer to the relationship between two variables, independent and dependent, and to various related notions, such as the differential.
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In the theory of relativit…
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The formula $$L=L_…
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The formula$$L=L_{0} \…
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Relativity According to th…
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In Einstein's theory …
This is problem or fifty six of the Stuart Calculus eighth edition, section two point three. In the theory of relativity, killer ends contraction formula ends. Hell equals al subzero. Time is a square root. Uh, the quantity one minus b squared over C squared This formula expressive the length l of an object as a function of its velocity. Be with respect in it and observer, where all subzero is the length of a dob. Check that rest and C is the speed of light. Find the limit and be a purchase See from the left with the function l ah and interpret the results. Why is the last time limit necessary? So let's answer the first question first. Well, we see that this functional is restricted by this square roots saying which it should be clear cannot take any negative numbers. It can't be that in mind. The domain of the square in here or a quantity inside of this square root needs to be, I reckon, greater than or equal to zero. This means that one must figure than equal to this racial and privately C squared needs to be greater than equal to V squared and at this point, we see that see must be greater than equal to B and in this way has via purchasing. We notice Avi is always less than thie. So we definitely are approaching C from the left. Now find this Lim. We approximate what we may be as a week approach. See? Well, it's used to excess institution one minus C squared over C squared. Excuse us. Screwed of one minus one. Which is, of course, zero. So the result is that and he doesn't want seen. So as your velocity approaches the speed of light the length of the object purchase zero. This means that the object essentially disappears as you approach on the speed of light.
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