Using the series expansions for and , find the first two non-zero terms in the Maclaurin series for .
Answer and explanation
Correct answer: D.
- Step 1: Write the standard series expansions: and .
- Step 2: Multiply the polynomial terms up to degree 3: .
Answer
.
Why not the others: The expression fails to cancel the opposite quadratic terms (); the linear expression drops the third-degree term; the expression subtracts rather than cancels the coefficients.
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