Question

so why cant a limit exist at 2 numbers or more, only one?

Answer 1

sorry, i dk.

Answer 2

I don't know what you mean by this but.

A limit only exists if the limit from the left and the limit from the right are equal.

Answer 3

hm ok, ill just take it as a rule, and understand it later then?

Answer 4

Limit exists if:
\[\lim_{x \rightarrow n^+} f(x) =\lim_{x \rightarrow n^-} f(x) \]

Answer 5

paul do you mean why can't a function approach two different numbers or more?
well there is left limit and there is a right limit
we say the limit does not exist if we do not have left limit=right limit (or if there is an infinite discontinuity)
when i say left limit it means what the function is approaching to the left of some number
when i say right limit it means what the function is approaching to the right of some number

Answer 6

Actually, if the function diverges then you can say that the limit is infinity. Although infinity is not a number it is used to describe a limit.

Answer 7

thanks myininaya, rephrasing it that way makes it sound more obvious (plus i didn't even understand what i was asking/understand limits really) so thanks

Alchemista, if i were to put that though, in an exam would i be able to say that it exists at infinity or -inf. ? or would i have to say it approaches infinity (or both +ve and -ve, depending on logarithmic, or exponential) and then proceed to say therefore it doesn't exist by definition of infinity which is an imaginary number.?

Answer 8

I think you are confusing the limit and "limit at".

For some function f(x) the limit at some value a is the limit of f(x) as x approaches a
\[\lim_{x \to a}f(x)\]

Answer 9

My point was if the function diverges to positive infinity or negative infinity from both sides at some point the limit is indeed infinity (either positive or negative)

Answer 10

oh i get that, im just trying to (now) find out the 'exam answer' if i were to get a quesiton that i would have to answer with infinity.