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Question
Find the coefficient of x4 in the expansion `(3 - 4x + x^2)/"e"^(2x)`
Solution
`(3 - 4x + x^2)/"e"^(2x) = (3 - 4x + x^2) "e"^(-2x)`
= `(3 -4x + x^2) [1 + (-2x)/(1!) + (-2x)^2/(∠2) + (-2x)^3/(∠3) ...]`
Coeffiient of x4: `3[(-2)^4/(4!)] - 4[(-2)^3/(3!)] + 1[(-2)^2/(2!)]`
= `3[16/24] + (- 4) ((- 8))/6 + 4/2`
= `48/24 + 32/6 + 2`
= `2 + 16/3 + 2`
= `(6 + 16 + 6)/3`
`28/3`
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