lim(x→2)x-2 /sin(

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lim(x→2)x-2 /sin(
lim(x→2)x-2 /sin(

lim(x→2)x-2 /sin(
答:
原式
=limx->2 (x^2-4)/[(x+2)sin(x^2-4)]
因为x->2,所以limx->2 x^2-4=0
所以limx->2 (x^2-4)/sin(x^2-4)=1
原式
=limx->2 1/(x+2)
=1/4

lim(x→2)(x-2) /sin( x^2-4)
=lim(x→2)(x^2-4) /(x+2)sin( x^2-4)
=lim(x→2)1/(x+2)*lim(x→2)(x^2-4) /sin( x^2-4)
=1/4*lim(x→2)(x^2-4) /sin( x^2-4)
令x^2-4=y则:y→0
所以原式:
=1/4*lim(y→0)y/siny
=1/4*1
=1/4.