Maths - series question? Can anyone help?

if we have two functions

f(x) = ln(3 + x)

g(x) = ln(1+x)

and by using ln(3+x) = ln3 + ln(1 + x/3),

we can show that ln(3 + x) = ln3 + x/3 - x^2/18 + x^3/27

given that you can write 1 + x = 3 + (x -2), and using the answer for the above question,

find the taylor series about 2 for g. Give the first three terms

1 Answer

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  • Awms A
    Lv 7
    1 decade ago
    Favorite Answer

    Okay... you just need to follow directions here...

    ln(3 + x) = ln3 + x/3 - x^2/18 + x^3/27

    So

    g(x) = ln(3 + (x-2) ) = the same as above, but with x replaced with (x-2).

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