The Taylor series of e^(6x) about x = 0 has the coefficient of x³ equal to
Answer and explanation
Correct answer: C. 36
- Step 1: e^(ax) = Σ (ax)ⁿ/n!, so the x³ term is a³x³/3!. Step 2. The coefficient is 216/6 = 36. Answer: 36. Why not the others: 72 is what you get if you divide by 3 instead of 3!. 1 is what you get if you forget to cube a. 18 is what you get if you give the coefficient of x².
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