x趋向于0 limf(x)=(x²-x)÷(x²-1) 为什么等于limx
来源:学生作业帮助网 编辑:作业帮 时间:2024/07/05 12:54:46
![x趋向于0 limf(x)=(x²-x)÷(x²-1) 为什么等于limx](/uploads/image/z/7109341-61-1.jpg?t=x%E8%B6%8B%E5%90%91%E4%BA%8E0+limf%28x%29%3D%EF%BC%88x%26%23178%3B-x%EF%BC%89%C3%B7%EF%BC%88x%26%23178%3B-1%EF%BC%89+%E4%B8%BA%E4%BB%80%E4%B9%88%E7%AD%89%E4%BA%8Elimx)
x趋向于0 limf(x)=(x²-x)÷(x²-1) 为什么等于limx
x趋向于0 limf(x)=(x²-x)÷(x²-1) 为什么等于limx
x趋向于0 limf(x)=(x²-x)÷(x²-1) 为什么等于limx
因为f(x)化简后就是 x÷x+1 等于0 而limx 当x趋向于0时也等于0 故是相等的
答:
lim(x→0) f(x)
=lim(x→0) (x²-x) / (x²-1)
=lim(x→0) x(x-1) /[ (x-1)(x+1)]
=lim(x→0) x /(x+1)
=lim(x→0) x/(0+1)
=x