lim(x²+1/3x-2)sinπ/2 (x趋于正无穷)=?lim(sinx/2x-xsinπ/x) (x趋于正无穷)=?
来源:学生作业帮助网 编辑:作业帮 时间:2024/10/08 09:15:35
xQNPBSZؖo".XTcbBCD!>h&|`,gܙ9儋̥kă}4G"źdy1g KCT)i#fEJb|;Χ+z'un"SZ>7zPYXPz٨ Z%2,d8
4l+AA_k74čH0Asc"%w__ˠ
5H*HSѯQ|Mer`>}ڙ7O %X6p,0;
9jV,ڪIt!ÅLjaZ`͍ڄ2MC:) 'h|"o?Zƿ
lim(x²+1/3x-2)sinπ/2 (x趋于正无穷)=?lim(sinx/2x-xsinπ/x) (x趋于正无穷)=?
lim(x²+1/3x-2)sinπ/2 (x趋于正无穷)=?lim(sinx/2x-xsinπ/x) (x趋于正无穷)=?
lim(x²+1/3x-2)sinπ/2 (x趋于正无穷)=?lim(sinx/2x-xsinπ/x) (x趋于正无穷)=?
第一题直接可以看出极限为正无穷
第二题运用无穷比无穷型极限求法:lim(sinx/2x-xsinπ/x)=limsinx/2x+limxsinπ/x
limsinx/2x中|sinx(x->无穷大)|≤1有界,而2x趋于无穷大,所以极限为0
limxsinπ/x=sinπ=0
所以lim(sinx/2x-xsinπ/x)=0
是不是少了几个括号啊?这么简单的?
第二问:lim(sinx/2x)=0,lim(xsinπ/x)=lim(sinπ/x)/(1/x)
=lim(sinπ/x)/(π/x)*π
而sinπ/x与π/x为x趋于正无穷时的等价无穷小,所以原式=0-π=-π