limit - Yacas apparently computes one-sided limit wrong

Question

I want to find

lim(x->4-) ((x-4)/(x^2-8*x+16))

so I typed this into the Yacas interface:

Limit(x,4,Right) (1/(x-4))

Yacas answered:

Infinity

But that is wrong; the answer is -Infinity. Am I just misunderstanding the dir argument of the Limit() function?

Answer 1

你只是弄乱了你的符号。回想一下微积分：

lim x goes to 4 of f(x) is two limits:
    lim x goes to 4- of f(x)
    lim x goes to 4+ of f(x)

如果这两个限制都存在，则 lim x 变为 4 存在。但是，您有向后的方向。x 到的 lim4-表示从左侧开始。x 到的 lim4+表示从右边开始。

Limit(x,4,Right) (1/(x-4)) == Infinity (lim x goes to 4+)
Limit(x,4,Left) (1/(x-4)) == -Infinity (lim x goes to 4-)