What is the first non-zero term in the Maclaurin series expansion of f(x) = ln(1 + x) - sin(x)?
Answer and explanation
Correct answer: D. -x^2 / 2
- Step 1: ln(1 + x) = x - x^2/2 + x^3/3 - ... and sin(x) = x - x^3/6 + ... Step 2. ln(1 + x) - sin(x) = (x - x^2/2 + x^3/3) - (x - x^3/6) = -x^2/2 + O(x^3). Answer: -x^2 / 2. Why not the others: The linear term x cancels out, leaving -x^2/2 as the leading term.
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