Question

does a limit exists when LHL and RHL both comes out to be infinity ?????

Answer 1

Please reiterate the definition.

Answer 2

yes, it exist and equals +infinity.

Answer 3

but infinity is not definite ..

Answer 4

infinity is defines as 1/0, or in terms of limits, very very large number.
the limit will not be defined only when LHL and RHL are unequal.

Answer 5

okay...ty again (Y)

Answer 6

welcome again (Y)

Answer 7

Really? Please reiterate the definition. L and R must _________ and be equal.

Answer 8

be defined ???

Answer 9

@tkhunny

Answer 10

"EXIST"

If it "approaches infinity", this means the limit does not exist. If it doesn't exist from either side, it doesn't magically exist - which is the definition we seem to be working with. That's just incorrect.

The limit exists if both the left and right limits exist (are finite) and are equal.

Answer 11

what i meant by "defined" was exist only....
i knew this fact but in some books the answers were --- that the limit exists because LHL=RHL (even if both were infinity.)
what i knew and what was written made me confused.
anyways thanks for confirming :-)

Answer 12

There is a text book that talks about Real Numbers and continuity that suggests unbounded right and unbounded left means the limit exists? I would find that a little surprising. If we were talking about finite geometries or various other things, it's okay for "infinity" to be "somewhere", but not just the Real Numbers.