Question: In Problems 29–34, determine the Taylor series about the point X0 for the given functions and values of X0.
32. f(x)=ln(1+x), x0 =0
The required expression is .
For a function f(x) the Taylor series expansion about a point x0 is given by,
We have to calculate the Taylor series expansion for,f (x)= ln (1 + x) at.
Calculating the derivatives of function at x0 ,
f (x) =ln (1+x) then f (x0)=0
f'(x) = then f '(x0) =1
f''(x) = then f''(x0) = -1
f'''(x) = then f'''(x0) = 2
f''''(x) = then f''''(x0) = -6
Substituting the above derivatives in Taylor series expansion for the function at , then,
= role="math" localid="1664200514125"
Hence, the required expression is
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