SOLUTION: Expand (1/4+2x) as a series of ascending powers of x up to the term x^3 and state the range of values of x for the expansion to be valid. Hence, use the expansion to approximate 1/
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Question 1184848: Expand (1/4+2x) as a series of ascending powers of x up to the term x^3 and state the range of values of x for the expansion to be valid. Hence, use the expansion to approximate 1/(4.05)^2 correct to 4 significant figures by taking a suitable value of x
Answer by robertb(5830) (Show Source): You can put this solution on YOUR website!
I will interpret you function as , since the function won't have a Taylor (Maclaurin) series that will even reach term.
It is straightforward exercise that .
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Up to the term, you get ~.
Letting x = 0.025, ~, or 0.0610 to 4 significant figures.
The Taylor expansion is valid for all , by the ratio test.
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