sinx=x−x33!+x55!−⋯\sin x =x-\dfrac{x^3}{3!}+\dfrac{x^5}{5!}-\cdotssinx=x−3!x3+5!x5−⋯ cosx=1−x22!+x44!−⋯\cos x =1-\dfrac{x^2}{2!}+\dfrac{x^4}{4!}-\cdotscosx=1−2!x2+4!x4−⋯ ex=1+x+x22!+x33!+⋯e^x=1+x+\dfrac{x^2}{2!}+\dfrac{x^3}{3!}+\cdotsex=1+x+2!x2+3!x3+⋯ log(1+x)=x−x22+x33−⋯\log(1+x)=x-\dfrac{x^2}{2}+\dfrac{x^3}{3}-\cdotslog(1+x)=x−2x2+3x3−⋯ ※ただし,log(1+x)\log (1+x)log(1+x) に関しては −1<x≦1-1
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