Devil's Sunrise Wrote:Strictly speaking, lim(x -> y) will never be equal for any limit as long the function's a "curve" (that is, f(x) = b, then lim(x -> y) = lim(x -> z). May be avoided by taking tops or bottoms of Sine or Cosine curves as well.)
...What? This doesn't make any sense. For one, what is lim(x -> y) not supposed to equal? You never say.
Devil's Sunrise Wrote:But actually, the answer is Infinity. Cause ey, what's Infinity multiplied by -1?
Negative infinity, which is a different number. :f6:
(Unless you're in a special geometry, and we aren't.)
Long story short, the answer is DNE, which is standard shorthand for Does Not Exist. The limit approaches two different values from either side of the point you're considering, so essentially, it doesn't "approach" anything at all in the sense you want... hence, Does Not Exist. Watch Mean Girls if you want Lindsey Lohan to confirm it for you... in an overly excited, valley girl kind of way.
EDIT: The answer isn't undefined. We say something is undefined when the question has been posed wrong... That's why 1/0 is undefined, because our system doesn't allow dividing by 0 anyway. This limit is a perfectly well-posed "question", it's just that the function in it happens to not be well-behaved at the point we're looking for.
That's why the term DNE exists. It's a fine point, though... The sort of thing math majors are interested in.