(16)
x->+∞
sin(1/x) = 1/x +o(1/x)
lim(x->+∞) [( x -1)/x]^[1/sin(1/x)]
=lim(x->+∞) (1 -1/x)^[1/sin(1/x)]
=lim(x->+∞) (1 -1/x)^[1/(1/x)]
=lim(x->+∞) (1 -1/x)^x
=e^(-1)
(13)
x->0
cosx = 1- (1/2)x^2 +o(x^2)
ln(cosx)=ln[ 1- (1/2)x^2 +o(x^2)] =-(1/2)x^2 +o(x^2)
lim(x->0) ln(cosx)/x^2
=lim(x->0) (-1/2)x^2/x^2
=-1/2
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