求极限lim(x趋向于0) (x-tanx)/xsinx^2

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求极限lim(x趋向于0)(x-tanx)/xsinx^2求极限lim(x趋向于0)(x-tanx)/xsinx^2求极限lim(x趋向于0)(x-tanx)/xsinx^2lim(x-tanx)/x

求极限lim(x趋向于0) (x-tanx)/xsinx^2
求极限lim(x趋向于0) (x-tanx)/xsinx^2

求极限lim(x趋向于0) (x-tanx)/xsinx^2
lim(x-tanx)/xsinx^2
=lim(x-tanx)/(x * x^2 * sinx^2 / x^2) 等价无穷小量:
=lim(x-tanx)/(x * x^2)
=lim(1/x^2 - sinx/x * 1/[x^2 * (cosx)]
=lim(1 - secx)/x^2 罗必塔法则:
=lim(-tanxsecx)/2x 罗必塔法则:
=-1/2limsecx(tan^2 x + sec^2 x)
=-1/2