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hi, i recently began learning about limits. however, i encountered a problem where i got two answers and i was unsure what to do:
l i m 1/(x-2)
(x->2)
so i made a table of values. of course, substitution of 2 gives indefinite...
but if you use the left hand limit then f(x) approaches negative infinity (-∞). i got this by getting functions of x for 1, 1.9, 1.99, 1.999... etc, and got -1, -10, -100, -1000, etc getting closer to negative infinity.
but here is what confuses me, if you use the right hand limit then f(x) approaches POSITIVE infinity, not negative infinity. so this leaves me with two answers, like i said before.
does that therefore mean the answer is 0, as the midpoint of negative infinity and positive infinity is 0? or are one of my answers, negative or positive infinity, correct?
sorry to bother you guys, i just started learning about limits, and i just dont understand what to do in this particular situation.
thanks for your help and taking the time to assist a poor friend in need!
A true limit exists only if the limits from both the left and the right sides exist and are equal. As you pointed out the limits from the left and right sides in your example are not equal, which means that the limit as a whole does not exist.
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oh ok, thanks.
so the answer would be indefinite?
ie, if this were to come up in an exam, my answer would be to write that lim(x->2) 1/(x-2) = indefinite?
The answer would be that the limit does not exist.
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If this appears in an exam simply write DNE for Does Not Exist, there are other ways to write this but that is the most common way...
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