Question

1/（sinx）^2-1/x^2的x趋于0的极限是多少,怎么算呢

Answer 1

lim(x→0){1/[(sinx)^2]-1/(x^2)}

= lim(x→0){[(sinx)^2]-(x^2)}/[(sinx)^2](x^2)

= lim(x→0){[(sinx)^2]-(x^2)}/(x^4) (0/0)

= lim(x→0)(2sinxcosx-2x)/(4x^3)

= lim(x→0)(sin2x-2x)/(4x^3) (0/0)

= lim(x→0)(2cos2x-2)/(12x^2)

= (2/3)lim(x→0)(cos2x-1)/[(2x)^2]

= ……

= -1/3