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近似公式
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x->0
分子
e^(cosx)
= e^[1-(1/2)x^2] +o(x^2)
=e. e^[(-1/2)x^2] +o(x^2)
=e.[ 1 -(1/2)x^2] +o(x^2)
e- e^(cosx) = (1/2)e.x^2 +o(x^2)
分母
(1+x^2)^(1/3) = 1+(1/3)x^2 +o(x^2)
(1+x^2)^(1/3) -1 =(1/3)x^2 +o(x^2)
/
lim(x->0) [e- e^(cosx) ]/[ (1+x^2)^(1/3) -1 ]
=lim(x->0) (1/2)e.x^2 /[ (1/3)x^2 ]
=(3/2)e
分子
e^(cosx)
= e^[1-(1/2)x^2] +o(x^2)
=e. e^[(-1/2)x^2] +o(x^2)
=e.[ 1 -(1/2)x^2] +o(x^2)
e- e^(cosx) = (1/2)e.x^2 +o(x^2)
分母
(1+x^2)^(1/3) = 1+(1/3)x^2 +o(x^2)
(1+x^2)^(1/3) -1 =(1/3)x^2 +o(x^2)
/
lim(x->0) [e- e^(cosx) ]/[ (1+x^2)^(1/3) -1 ]
=lim(x->0) (1/2)e.x^2 /[ (1/3)x^2 ]
=(3/2)e
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