Pure Maths - limit

👨🏻‍🏫 學術台數學

[匿名]

2009-08-06 6:27 pm

If lim of f(x) at x = a is infinity
and lim of f(x) at x = a is infinity,
is it true that lim of [f(x) g(x)] at x = a is infinity?

Thanks.

更新1:

If lim of f(x) at x = a is infinity and lim of g(x) at x = a is infinity, is it true that lim of [f(x) g(x)] at x = a is infinity? Thanks.

回答 (3)

myisland8132

2009-08-06 9:39 pm

✔ 最佳答案

我覺得第二行和第三行都有問題
第二行是g(x)﹐第三行是f(x)/g(x)
∞*∞=∞ 所以 lim [f(x) g(x)] at x = a
= lim [f(x)] lim [g(x)] at x = a
= ∞*∞
= ∞
但 ∞/∞ 是無定義﹐所以要用洛必達法則。
螞蟻雄兵該答案中的 lim [g(x)] at x = 0 = lim [x] at x = 0 = 0 不是 ∞

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用戶8745

2009-08-06 9:34 pm

I think there is a typo error in the question.
In the second line, f(x) should be g(x).

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螞蟻雄兵

2009-08-06 7:19 pm

If lim of f(x) at x = a is infinity，and lim of f(x) at x = a is infinity,
is it true that lim of [f(x) g(x)] at x = a is infinity?
Sol
We can not sure ,so it is not true.
example
lim(x->0)_1/x^2 =inifite
lim(x->0)_[(1/x^2)*x^2]=1

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