圖片參考：http://imgcld.yimg.com/8/n/HA04937267/o/701204240023513873398630.jpg
evaluate the following limits.(唔洗計,我有ans)
(a)lim x->0 [xf(2x)]
(b)lim x->0 [(x^3)f(x^2)]
問題:
上面幅圖到
lim x->0 [xf(x)] (x是independent variable)
= (lim x->0 x)[lim x->0 f(x)]
=0
點解題目會寫lim x->0 [xf(x)]=1?
有無example可以提供?
定係我計錯?
更新1:
謝謝回答 其實我計到a同b 我只是不懂為甚麼 lim x->0 [xf(x)] =/= (lim x->0 x)[lim x->0 f(x)] 因為書中曾提及其中一個property lim x->a [f(x)g(x)] = [lim x->a f(x)][lim x->a g(x)] 套用在這的話 就是 lim x->0 [xf(x)] = (lim x->0 x)[lim x->0 f(x)] 有甚麼地方錯了?