sqrt.[(1+x)/(1-x)]=(1+x)/sqrt.(1-x^2)=(1+x)*(1-x^2)^-(1/2)
=(1+x)*[1-(-1/2)*x^2]
=(1+x)*[1+x^2/2]
=1+x+x^2/2+x^3/2.
question 2>take x=0.01,u get,97^(3/2)/1000.
How is that helping prove that the approx expansion is: 1+x+(1\2)x^2?
I had sqrt((1+x)/(1-x)) = ((1+x)^(1/2))*((1-x)^(-1/2))
I expanded those up to x^1 and got (1+(1/2)x)*(1+(1/2)x) using the binomial theorem, then that expands to 1+x+(1/4)x^2, very close to the answer, wondering if the book got it wrong..