limx→0(tanx-sinx)/x∧3
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解决时间 2021-03-24 07:37
- 提问者网友：刺鸟
- 2021-03-23 10:42
limx→0(tanx-sinx)/x∧3
最佳答案
- 五星知识达人网友：老鼠爱大米
- 2021-03-23 11:31
lim(x→0) (tanx-sinx)/x∧3
=lim(x→0) (sinx/cosx-sinx)/x∧3
=lim(x→0) (1/cosx-1)/x∧2 * (sinx/x)
=lim(x→0) (1-cosx)/x∧2 /cosx
=lim(x→0) (1-cosx)/x∧2
=lim(x→0) 2 (sin (x/2) )^2/x∧2
=lim(x→0) 2(x/2)^2/x∧2
=1/2
=lim(x→0) (sinx/cosx-sinx)/x∧3
=lim(x→0) (1/cosx-1)/x∧2 * (sinx/x)
=lim(x→0) (1-cosx)/x∧2 /cosx
=lim(x→0) (1-cosx)/x∧2
=lim(x→0) 2 (sin (x/2) )^2/x∧2
=lim(x→0) 2(x/2)^2/x∧2
=1/2
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