J's answer to mint's Junior College 2 H2 Maths Singapore question.
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Using your MF26 formulas,
eˣ cos x = (1 + x + x²/2! + x³/3! + ...) (1 - x²/2! + x⁴/4! - ...)
You only need up to x³, so extract the relevant products.
= (1)(1) - 1(x²/2!) + x(1) + x(-x²/2!) + x²/2! (1) + x³/3! (1) + ...
= 1 - ½x² + x - ½x³ + ½x² + 1/6 x³ + ...
= 1 + x - 1/3 x³ + ...
≈ 1 + x - 1/3 x³
The answer option is incorrect.
eˣ cos x = (1 + x + x²/2! + x³/3! + ...) (1 - x²/2! + x⁴/4! - ...)
You only need up to x³, so extract the relevant products.
= (1)(1) - 1(x²/2!) + x(1) + x(-x²/2!) + x²/2! (1) + x³/3! (1) + ...
= 1 - ½x² + x - ½x³ + ½x² + 1/6 x³ + ...
= 1 + x - 1/3 x³ + ...
≈ 1 + x - 1/3 x³
The answer option is incorrect.
Date Posted:
3 years ago
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