lim(secx-1)^2/3x^2sinx^2=?当x趋于0时
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![lim(secx-1)^2/3x^2sinx^2=?当x趋于0时](/uploads/image/z/8805525-69-5.jpg?t=lim%28secx-1%29%5E2%2F3x%5E2sinx%5E2%3D%3F%E5%BD%93x%E8%B6%8B%E4%BA%8E0%E6%97%B6)
lim(secx-1)^2/3x^2sinx^2=?当x趋于0时
lim(secx-1)^2/3x^2sinx^2=?当x趋于0时
lim(secx-1)^2/3x^2sinx^2=?当x趋于0时
x趋于0的时候,sinx是等价于x的,
而
secx-1=1/cosx -1=(1-cosx)/cosx
显然
x趋于0时,1-cosx等价于0.5x^2,而cosx趋于1
所以secx-1等价于0.5x^2
故
原极限
=lim(x趋于0) (0.5x^2)^2 / (3x^2 *x^2)
=1/12