Infinity limits in calculus?

Question

If I evaluate a limit of a function to be positive or negative infinity, should I state that the limit DNE or should I state positive/negative infinity. My teacher said that we should write DNE but he wasn't very clear and the answer key in the book write positive/negative infinity.

Answer 1

When a function goes to positive or negative infinity it means that it increases or decreases without bound and does not converge to a certain number. So when you say the limit as x aproaches infinity is infinity, you're essentially saying that the limit does not exist since it doesn't converge to a number. So I think either is right

Answer 2

Typically if a limit is an extended real number i.e., +/- infinity it's acceptable to write that the limit does not exist.

Answer 3

+ve or -ve infinity, although your teacher may just like you to write it in his own notation.



I haven't come across DNE, but I can only imagine it stands for does not evaluate.

Answer 4

i 'd write + or - infinity