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The linear approximation to 1/sqrt(3-x) at

x=0 is y=

1 answer

(3-x)^(u) =

3^u (1 - x/3)^u =

3^u [1 - u (x/3) + u (u-1)/2 (x/3)^2 - u (u-1)(u-2)/6 (x/3)^3 + ....]

Insert u = -1/2 in here to obtain:

1/sqrt(3-x) =

1/sqrt(3) [1 + x/6 + x^2/24 +
5 x^3/432 + ... ]

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