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Q: Find the Fourier transform of f(t) = e^(-2|t|). F(ω) = ∫_{-∞}^0e^(2t)e^(-iωt)dt+∫₀^∞e^(-2t)e^(-iωt)dt. = 1/(2-iω)+1/(2+iω) = 4/(4+ω²). Check: even function: real transform ✓! (Width tradeoff: narrow time, wide frequency!)