Homework, section 1.6
MAT129
Andy Long
#34, #54

#34:

f[x_]:=(Sqrt[3+x]-Sqrt[3])/x
Plot[f[x],{x,-1,1}]

TableForm[Table[{x,N[f[x]]},{x,-.01,.01,.02/17}]]
Limit[f[x],x->0]

For the limit laws, use the conjugate.

#36: squeeze it:

f[x_]:=Sqrt[x^3+x^2]Sin[Pi/x]
g[x_]:=Sqrt[x^3+x^2]
Plot[{-g[x],f[x],g[x]},{x,-1,1}]

#54: Lorentz contraction

In the limit as v -> c, the argument under the square root sign goes to 0, so L goes to 0. The length contracts.

The left-hand limit is necessary because nothing travels faster than the speed of light. It’s the intergalactic speed limit.