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?

score 1 · Accepted Answer · answered Oct 07 '14 at 20:00

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-)

graph of y = 1/(x-4)

answered Oct 07 '14 at 20:00

royhowie

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Thanks, Roy, that makes sense. The Yacas manual is written backwards for Limit(); it says 'If one gives "dir" the value Left, the limit is taken as "var" approaches "val" from the positive infinity; and Right will take the limit from the negative infinity.' – Steve Pfeiffer Oct 07 '14 at 20:24
@StevePfeiffer What does it say? – royhowie Oct 07 '14 at 20:26
Sorry hit "Return" too soon – Steve Pfeiffer Oct 07 '14 at 20:27
@StevePfeiffer That's really weird. – royhowie Oct 07 '14 at 20:32

Yacas apparently computes one-sided limit wrong

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