求极限(sin(2/n)+cos(3/n))^(-n)

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求极限(sin(2/n)+cos(3/n))^(-n)
求极限(sin(2/n)+cos(3/n))^(-n)

求极限(sin(2/n)+cos(3/n))^(-n)
lim(n→∞)[(sin(2/n)+cos(3/n))^(-n)]
=lim(n→∞)[(sin(2/n)+1)^(-n)]
=e^[lim(n→∞)(-n)ln(sin(2/n)+1)](等价无穷小替换)
=e^[lim(n→∞)(-n)(sin(2/n)]
=e^{lim(n→∞)(-2)[(sin(2/n))/(2/n)]}
=e^(-2)

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