求极限lim(x趋近9)sin²x-sin²9/x-9
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![求极限lim(x趋近9)sin²x-sin²9/x-9](/uploads/image/z/1697272-16-2.jpg?t=%E6%B1%82%E6%9E%81%E9%99%90lim%28x%E8%B6%8B%E8%BF%919%29sin%26%23178%3Bx-sin%26%23178%3B9%2Fx-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