| e^x - 1 = ∫[0,x]e^t dt = [(t-x)e^t](t:0,x) - ∫[0,x](t-x)e^tdt = x + ∫[0,x](x-t)e^tdt = x + [-(1/2)(x-t)^2 e^t](0,x) + ∫[0,x](1/2)(x-t)^2 e^tdt = x + (1/2)x^2 + ∫[0,x](1/2)(x-t)^2 e^tdt
0<x<1 とすると |e^x - 1 - x - (1/2)x^2| = ∫[0,x](1/2)(x-t)^2 e^t dt <∫[0,x](1/2)(x-t)^2 e^1 dt = e[-(1/3!)(x-t)^3](t:0,x) = (e/3!)x^3
|(e^x - 1 - x)/x^2 - 1/2|<(e/3!)x → 0 ( x → +0 )
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