(x→0)lim(x-ln(1+tanx))/(sinx)∧2=?

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(x→0)lim(x-ln(1+tanx))/(sinx)∧2=?(x→0)lim(x-ln(1+tanx))/(sinx)∧2=?(x→0)lim(x-ln(1+tanx))/(sinx)∧2=?x

(x→0)lim(x-ln(1+tanx))/(sinx)∧2=?
(x→0)lim(x-ln(1+tanx))/(sinx)∧2=?

(x→0)lim(x-ln(1+tanx))/(sinx)∧2=?

x趋于0时,(sinx)^2=x^2,ln(1+tanx)=tanx-tan^2x/2
而tanx也与x等价,
因此原式=(x-tanx)/x^2 +1/2,再对前面一项用洛必达法则即可