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In the theory of relativity, the mass of a particle with velocity $ v $ is$$ m = \frac{m_0}{\sqrt{1 - v^2/c^2}} $$where $ m_0 $ is the mass of the particle at rest and $ c $ is the speed of light. What happens as $ v \to c^- $?

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02:40

Daniel Jaimes

Calculus 1 / AB

Chapter 2

Limits and Derivatives

Section 2

The Limit of a Function

Limits

Derivatives

Campbell University

Harvey Mudd College

Baylor University

Boston College

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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Relativity According to th…

Okay. So M is the mass of an object and M sub not. Is the initial mass How much it way before he started moving around? Okay. V is the velocity of the mass and C. Is the speed of light? So the question is, what happens to this mass? This mass as your as its velocity approaches the speed of light? I put a little minus sign there because I mean I'm approaching it from numbers less than it. Because we have to slowly get up. We have to come from a slower speed to get to see. Okay, so as we get close to see then what happens to V squared over C squared? Well B and C are almost the same then V squared over C squared is almost one. Okay, so we have um sub zero over the square to one minus one nipple. Little minus sign here and buy this minus. I mean the same thing. It's a little bit less than one. Okay, so the bottom is one minus something. A tiny little bit less than it. So that's zero. Okay, but it's positive zero. It's a little bit bigger than zero because this is a little bit smaller than one. So it's square root is a little bit bigger than zero. So what happens if you have a number and you divide it by a tiny tiny tiny little thing. That's almost zero. Well it goes to infinity infinite mass. As its velocity approaches the speed of light, its mass becomes infinite

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