作业帮lim(1-X*X/2)的1/sinX*sinX次方（X趋向0）
来源：学生作业帮 编辑：作业帮 分类：数学作业 时间：2024/11/07 23:40:30
lim(1-X*X/2)的1/sinX*sinX次方（X趋向0）
lim(1-X*X/2)的1/sinX*sinX次方（X趋向0）
=lim(x--->0)(1-1/2*x^2)^((sinx)^2)
=lim(x--->0)(e^(ln(1-1/2*x^2)/(sinx)^2)
=e^(lim(x--->0)(ln(1-1/2*x^2)/(sinx)^2
x--->0时,sinx--->x
=e^(lim(x--->0)(ln(1-1/2*x^2)/x^2)
=e^(lim(x--->0)((-x/(1-1/2*x^2))/2x)
=e^(lim(x--->0)(-1/(2-x^2))
=e^(-1/2)
=lim(x--->0)(1-1/2*x^2)^((sinx)^2)
=lim(x--->0)(e^(ln(1-1/2*x^2)/(sinx)^2)
=e^(lim(x--->0)(ln(1-1/2*x^2)/(sinx)^2
x--->0时,sinx--->x
=e^(lim(x--->0)(ln(1-1/2*x^2)/x^2)
=e^(lim(x--->0)((-x/(1-1/2*x^2))/2x)
=e^(lim(x--->0)(-1/(2-x^2))
=e^(-1/2)
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