求极限lim(x趋近9)sin²x-sin²9/x-9

求极限lim(x趋近9)sin²x-sin²9/x-9
求极限lim(x趋近9)sin²x-sin²9/x-9

求极限lim(x趋近9)sin²x-sin²9/x-9
原式=lim(x→9) (sinx+sin9)(sinx-sin9)/(x-9)
=lim(x→9)(sinx+sin9)*lim(x→9)(sinx-sin9)/(x-9)
=2sin9*lim(x→9) 2sin[(x-9)/2]cos[(x+9)/2]/(x-9)
=4sin9*lim(x→9) cos[(x+9)/2]*lim(x→9) sin[(x-9)/2]/(x-9)
=4*sin9*cos9*(1/2)
=sin18