# Question:Dutch math book comparing two functions with a taylor series

## Question:Dutch math book comparing two functions with a taylor series

Maple

Hello everyone,

The "rows and series" chapter is coming to an end. But im not getting this question. Ive got a feeling they are not really specific with this book. But that could just be me.

Any way here is the question:

"In classical physics there is the kinetic energy of a body with the mass m0 and the speed v given by E1=1/2*m0*v^2. According to Einstein the kinetic energy E2=(m*c^2)-(m0*c^2)=((m0*c^2)/sqrt(1-(v/c)^2))-m0*c^2, at which m is the relativistic mass with a speed v, and m0 the mass in rest. Further c is the speed of light. Wright down E2 as a linear function of v^2 and show that E2=E1 when v is small compared to c."

Now i cant see what they did to get this answer:

A taylor series was probably used, the question before it also used a taylor series.

If someone knows what they did. What did they do to get the the answer the book gave?

Thank you!

Greetings,

The Function

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