limx→0(tanx-sinx)/x∧3
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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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