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

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