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

You're just messing up your notation. Think back to calculus:

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)

If both of those limits exist, then lim x goes to 4 exists. However, you have the directions backwards. The lim as x goes to 4- means from the left. The lim as x goes to 4+ means from the right.

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-)