一道数学题,关于极限的.
来源:学生作业帮 编辑:搜搜做题作业网作业帮 分类:数学作业 时间:2024/07/15 21:08:12
一道数学题,关于极限的.
![](http://img.wesiedu.com/upload/0/b1/0b123b1930cba7dffe3cf26031f13b17.jpg)
![](http://img.wesiedu.com/upload/0/b1/0b123b1930cba7dffe3cf26031f13b17.jpg)
![一道数学题,关于极限的.](/uploads/image/z/8674247-47-7.jpg?t=%E4%B8%80%E9%81%93%E6%95%B0%E5%AD%A6%E9%A2%98%2C%E5%85%B3%E4%BA%8E%E6%9E%81%E9%99%90%E7%9A%84.)
原式
= lim (x^3 + tan x - sinx)/x^3
= 1 + lim (tanx -sinx)/x^3
= 1+ lim sinx(1/cosx -1)/x^3
= 1 + lim (1/cosx -1)/x^2
= 1 + lim (1-cosx)/x^2
= 1+ lim (1- (1-2(sinx/2)^2))/x^2
= 1+ lim 2(sinx/2)^2/x^2
= 1+ lim 2 (x/2)^2 /x^2
= 1 + 1/2
= 3/2
= lim (x^3 + tan x - sinx)/x^3
= 1 + lim (tanx -sinx)/x^3
= 1+ lim sinx(1/cosx -1)/x^3
= 1 + lim (1/cosx -1)/x^2
= 1 + lim (1-cosx)/x^2
= 1+ lim (1- (1-2(sinx/2)^2))/x^2
= 1+ lim 2(sinx/2)^2/x^2
= 1+ lim 2 (x/2)^2 /x^2
= 1 + 1/2
= 3/2