13问答网 > 1⼀（sinx）^2-1⼀x^2的x趋于0的极限是多少，怎么算呢

1⼀（sinx）^2-1⼀x^2的x趋于0的极限是多少，怎么算呢

答案是三分之一，请大家赐教

2025-03-10 08:43:06

推荐回答（1个）

回答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