利用导数的定义求下列极限谢谢!
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:2024/07/08 17:30:39
利用导数的定义求下列极限谢谢!
![](http://img.wesiedu.com/upload/e/0c/e0c6adba69988fd7b60e43370412795f.jpg)
![](http://img.wesiedu.com/upload/e/0c/e0c6adba69988fd7b60e43370412795f.jpg)
![利用导数的定义求下列极限谢谢!](/uploads/image/z/3171744-0-4.jpg?t=%E5%88%A9%E7%94%A8%E5%AF%BC%E6%95%B0%E7%9A%84%E5%AE%9A%E4%B9%89%E6%B1%82%E4%B8%8B%E5%88%97%E6%9E%81%E9%99%90%E8%B0%A2%E8%B0%A2%21)
lim(h→0)[f(x0+h)-f(x0-h)]/h
=lim(h→0)[f(x0+h)-f(x0)+f(x0)-f(x0-h)]/h
=lim(h→0){[f(x0+h)-f(x0)]-[f(x0-h)-f(x0)]}/h
=lim(h→0)[f(x0+h)-f(x0)]/h+lim(h→0)[f(x0-h)-f(x0)]/(-h)
=f`(x0)+f`(x0)
=2f`(x0)
=lim(h→0)[f(x0+h)-f(x0)+f(x0)-f(x0-h)]/h
=lim(h→0){[f(x0+h)-f(x0)]-[f(x0-h)-f(x0)]}/h
=lim(h→0)[f(x0+h)-f(x0)]/h+lim(h→0)[f(x0-h)-f(x0)]/(-h)
=f`(x0)+f`(x0)
=2f`(x0)