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2019-01-28 · 中小学教师,杨建朝,蒲城县教研室蒲城县教育学会、教育领域创作...
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凑重要不等式lim_{x→∞}(1+1/x)^x
以下省略{x→∞}
lim(x-2/x+2)^x
=lim((x+2-4)/(x+2))^x
=lim(1+(-4)/(x+2))^x
=lim(1+(-4)/(x+2))^x
=lim(1+(-4)/(x+2))^((x+2)/-4)*((-4)/(x+2))*x
=lime^((-4)/(x+2))*x
=lime^((-4x)/(x+2)) 指数部分上下同除x
=lime^((-4)/(1+2/x))
=e^-4
以下省略{x→∞}
lim(x-2/x+2)^x
=lim((x+2-4)/(x+2))^x
=lim(1+(-4)/(x+2))^x
=lim(1+(-4)/(x+2))^x
=lim(1+(-4)/(x+2))^((x+2)/-4)*((-4)/(x+2))*x
=lime^((-4)/(x+2))*x
=lime^((-4x)/(x+2)) 指数部分上下同除x
=lime^((-4)/(1+2/x))
=e^-4
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