The Taylor series for $$\(\ln (1+2 x)\)$$ about $$\(x=0\)$$ is

A.
\(2 x-2 x^{2}+\frac{8}{3} x^{3}-4 x^{4}+\cdots\)
B.
\(2 x-4 x^{2}+16 x^{3}+\ldots\)
C.
\(2 x-x^{2}+\frac{8}{3} x^{3}-4 x^{4}+\cdots\)
D.
\(2 x-2 x^{2}+\frac{4}{3} x^{3}-\frac{2}{3} x^{4}+\cdots\)
Calculus
AP
College Board
Exam No:AP Calculus Unit 10 Questions Set Year:2024 Question No:35

Answer:

A

Knowledge points:

10.14 Finding Taylor or Maclaurin Series for a Function
10.15 Representing Functions as Power Series

Solution:

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