=lim (2sin^2 x/2) /x^2为什么等于 1/2 lim (sin^2 x/2)/(x/2)^2

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=lim(2sin^2x/2)/x^2为什么等于1/2lim(sin^2x/2)/(x/2)^2=lim(2sin^2x/2)/x^2为什么等于1/2lim(sin^2x/2)/(x/2)^2=lim

=lim (2sin^2 x/2) /x^2为什么等于 1/2 lim (sin^2 x/2)/(x/2)^2
=lim (2sin^2 x/2) /x^2为什么等于 1/2 lim (sin^2 x/2)/(x/2)^2

=lim (2sin^2 x/2) /x^2为什么等于 1/2 lim (sin^2 x/2)/(x/2)^2

因为因为x²=4*(x/2)²
所以lim (2sin² x/2) /x²=lim (2sin² x/2)/[4(x/2)²]=lim (sin² x/2)/[2(x/2)²]=(1/2)lim (sin² x/2)/(x/2)²
再利用limsin(x/2)/(x/2)=1(x→0)来求极限