Difference between relatavistic kinetic energy and normal kinetic energy

Kennalj
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I was looking at the relativistic energy of an electron and noticed that the formula for kinetic energy is:

K.E. = mc^2 -m0c^2


How is this related to the kinetic energy for low speed particles?
Does anyone have a link to the proof?
 
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This can be written as (Gamma - 1) m_0c^2. Do a taylor expansion of gamma and the result immediately follows.
 

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