求lim((sin²x-sin²9)/(x-9)),x→9 lim((x+n)/(x-n))的x次方,x→∞

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求lim((sin²x-sin²9)/(x-9)),x→9 lim((x+n)/(x-n))的x次方,x→∞
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求lim((sin²x-sin²9)/(x-9)),x→9 lim((x+n)/(x-n))的x次方,x→∞
求lim((sin²x-sin²9)/(x-9)),x→9 lim((x+n)/(x-n))的x次方,x→∞

求lim((sin²x-sin²9)/(x-9)),x→9 lim((x+n)/(x-n))的x次方,x→∞
第一题x→9时为0/0型,使用罗比达法则;第二题使用重要极限(1^∞型),

lim((sin²x-sin²9)/(x-9)), x→9
=2[cosx(x+9)/2sinx(x-9)/2]/(x-9)
sinx(x-9)/2 ~(x-9)/2

2[cosx(x+9)/2*(x-9)/2]/(x-9)
=cos9
lim((x+n)/(x-n)) x→∞
=lim((1+n/x)/(1-n/x))
n/x~0 x→∞
=1