(1)
x->0
cos(x^3) ~ 1- (1/2)x^6
1-cos(x^3) ~ (1/2)x^6
lim(x->0) [1-cos(x^3)]/[ x^3.(sinx)^3)]
=lim(x->0) (1/2)x^6/ x^6
=1/2
(8)
xy=a^2
xy' + y = 0
y' = -y/x
切线方程 (x0, y0)
y-y0= f'(x0) (x-x0)
y-y0= -(y0/x0) (x-x0)
y- a^2/x0 = - (a^2/x0^2) (x-x0)
x=0 , y=2a^2/x0
y=0 , x= 2x0
三角形面积 =(1/2)xy = (1/2) [2a^2/x0] [2x0) = 2a^2
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