Einstein's theory of relativity predicts that a body of mass m0 at rest has mass: m = m0/√(1-(v^2/c^2)) , where c is the velocity of light and v is the velocity of the body.
Use a series to obtain the approximation: mc^2 ≈ m0c^2 + 1/2m0v^2
Other Info that may be needed:
1. Mass energy formula: E = mc^2
2. Kinetic energy of a body at rest: v = 1/2m0v^2 (where mass is m0 and velocity is v)
I am so sorry about this. your probably getting frustrated at me. To show work in my problem, I am not sure how to go from the McLaurin series to being able to show that the series is the approximation. How did you arrive at the fact that the McLaurin series is the approximation? Sorry again but I need to show tons of work for these problems.
Im in Calc II. I know about power series but I am just not getting the jist of this problem. I understand about the series that I have to use. I am just confused on what to plug into it. Do I do a ratio or root test to it? I am just confused on how I can use that series to approximate Einstein's theory.
Captain has correctly specified what you have to do, and Mathstud28 continued with the definition of McLaurin series to help you.
Clearly f(0) = 1,
Then do a little computation to obtain f''(0) = 1.
Now from Mathstud28's formula
But from the previous approximation if we let , we get:
Substituting this in we get,