let's take2 functions to compare and contrast: f(x) = x/abs(x) g(x) = 1/x^2 both concern the correct wording when describing what happens as x--> 0
in the case of f it is clear to me that the limit does not exist since the right hand limit differs from the left hand limit.
in the case of g from the left it approaches positive infinity and from the right it approaches positive infinity. Would it be in correct to state for g that "limit does not exist" i.e. if this were a question on the AP exam would the scoring guide say that the student must state positive infinity (all other answers not acceptable).
I was under the impression that the definition of limit requires that the left and right limit to approach the *same number* L and infinity is clearly not a number. However, in the case of function g the left and right limits are approaching the same thing albeit not a number L.
Does College Board make a distinction between the phrase limit does not exist, limit approaches infinity, and a third variant "no limit"
Is there a mathematical/technical distinction between these three phrases.
Finally, if you look at h(x) = 1/x x-->0 can you simply state the limit does not exist? The limit from the left is negative infinity, the limit from the right is positive infinity.
My personal opinion is that DNE should be the catch all phrase for when the function does not approach some fixed number L but I'm asking for clarification in case I'm or have misinterpreted the definition.