Find the first three terms of the Maclaurin series for f(x) =
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Step-by-step explanation:

Starting out with the Taylor series,

where is the nth derivative of f(x) and if we set a = 0, we get the special case of the Taylor series called the Maclaurin series:

Expanding this series up to the 1st 3 terms at a = 0,

Let's find the derivatives of :

We can now write the Maclaurin series for as

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step-by-step explanation:

x =±sqrt(1/3)

step-by-step explanation:

x+4/6x=1/x

multiply each side by 6x to get rid of the fractions

6x*(x+4/6x)=1/x*6x

distribute

6x^2 +4 = 6

subtract 4 from each side

6x^2 +4-4 = 6-4

6x^2 =2

divide by 6

6x^2/6 = 2/6

x^2 = 1/3

take the square root of each side

sqrt(x^2) = ±sqrt(1/3)

x =±sqrt(1/3)