SOLUTION: please help me on the following qn: Obtain the first four terms of the expansion of (1+8x)^0.5 in ascending powers of x by putting x=0.01, obtain the value of (3)^0.5 correct

Algebra ->  Permutations -> SOLUTION: please help me on the following qn: Obtain the first four terms of the expansion of (1+8x)^0.5 in ascending powers of x by putting x=0.01, obtain the value of (3)^0.5 correct       Log On


   

Question 1091387: please help me on the following qn:
Obtain the first four terms of the expansion of (1+8x)^0.5 in ascending powers of x by putting x=0.01, obtain the value of (3)^0.5 correct to five decimal places
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
%281%2B8x%29%5E%280.5%29=1%2B4x-8x%5E2%2B32x%5E3
So then substituting,
%281%2B8%280.01%29%29%5E%280.5%29=1%2B4%280.01%29-8%280.01%29%5E2%2B32%280.01%29%5E3
sqrt%281.08%29=1%2B%280.04%29-%280.0008%29%2B%280.000032%29
sqrt%281.08%29=1.039232%29
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1%2B8x=3
8x=2
x=1%2F4
However, the Taylor series expansion at x=0 only converges when abs%288x%29%3C1
abs%28x%29%3C1%2F8