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GATE 2024 Chemical Engineering, Q11 · Mathematics

The correct answer is D, −x²/2.

Question

The first non-zero term in the Taylor series expansion of (1 − x) −e−x− e^{−x} about x = 0 is

  • A. 1
  • B. −1
  • C. x2/2x²/2
  • D. −x2/2−x²/2

Official answer: −x2/2−x²/2

Why

GATE 2024 official key: (D). (1−x) −e−x=− e^{−x} = (1−x) − (1 − x +x2/2−x3/6++ x²/2 − x³/6 + ⋯) =−x2/2+x3/6−= −x²/2 + x³/6 − ⋯, so the constant and linear terms cancel, leaving −x2/2−x²/2 as the first non-zero term.

Explanation cross-checked for consistency. Final answer matches the official IIT answer key.

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