lim(x→0)[∫(0,x)(e^(t^2)-1)dt]/x^3
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lim(x→0)[∫(0,x)(e^(t^2)-1)dt]/x^3
lim(x→0)[∫(0,x)(e^(t^2)-1)dt]/x^3
lim(x→0)[∫(0,x)(e^(t^2)-1)dt]/x^3
用罗必塔吧
lim(x→0)[∫(0,x)(e^(t^2)-1)dt]/x^3
=lim(x→0)[e^(x^2)-1]/3x^2 令u=x^2
=lim(u→0)[e^u-1]/3u
=lim(u→0)e^u/3
=1/3
lim(x→0)[∫(0,x)(e^(t^2)-1)dt]/x^3
=lim(x→0)(e^(x^2)-1)/3x^2
=lim(x→0)2xe^(x^2)/6x
=1/3
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