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

来源:学生作业帮助网 编辑:作业帮 时间:2024/12/01 08:23:30
求lim((sin²x-sin²9)/(x-9)),x→9 lim((x+n)/(x-n))的x次方,x→∞
xj@_%,lW2h7e&MfbEJDBXm}vRjϜqvjܩ8Y3|h Ez8yi ,u+_SI5%Av`0:x8yFU_Gvct}q|[~9;>.:Mg&[>lދ鰇nKiY>>mNYѼUn-{O,}M<uUVgQM౿x>Ohܠ.6 Wע4A fa9l"l+`&$&5@"#0"6QN&b3/3Zdlz!C ^sqGmb蚚zpҼ×i,B1ߪ`;6J7+PpejxiUJ@Z)h^ѹ|U

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