lim(x趋近于0)(cos2x-cos3x)/x²

问题描述:

lim(x趋近于0)(cos2x-cos3x)/x²

答:5/2用洛必达法则:lim(x-->0) (cos2x - cos3x)/x²= lim(x-->0) (- 2sin2x + 3sin3x)/(2x)= lim(x-->0) (- 4cos2x + 9cos3x)/(2)= (- 4 + 9)/2 = 5/2用和差化积公式:lim(x-->0) (cos2x - cos3x)/x²= l...从(cos2x - cos3x)怎样用和差化积公式化成- 2[sin(5x/2)sin(- x/2)]?cosA - cosB = - 2sin(A/2 + B/2)sin(A/2 - B/2)