Calculus Problem!!!Help hav test in 2days!!!!!?

Question

A).write out the first four terms in the power series expansion of (1-x)1/2(that should be a half btw!)in ascending powers of x

part B).use the expansion obtained in part a),wit x=0.02,to estimate(ok i cant find the square root button c**p!!sorry) square root shud be on top of tis!! 0.98 sorry!!!hope u get d idea!!!

Answer 1

I did this by finding the Maclaurin series for f(x) = (1-x)^1/2

f(0) = 1

f ' (0) = -1/2

f '' (0) = -1/4

f ''' (0) = -3/8

(1-x)^1/2 ≈ 1 - x/2 - (x^2)/(4*2!) - (3*x^3)/(8*3!) - ... {simplifying this gives -> }

(1-x)^1/2 ≈ 1 - x/2 - (x^2)/8 - (x^3)/16 - ...

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Actual value of (0.98)^1/2 ≈ 0.989949

Putting x = 0.02 in the Maclaurin series gives (0.98)^1/2 ≈ 0.989950