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Left and Right Hand limit of a Piece wise function?
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[QUOTE="LCKurtz, post: 4469496, member: 198114"] To answer your last question first, you don't use the third rule because you are interested in values of ##x## near ##2## and the third rule is irrelevant to that. You don't evaluate limits by plugging in the value unless you know the functions you are using are continuous. But in your case they are both polynomials. Assuming you have the theorem for polynomials ##p(x)## that$$ \lim_{x \rightarrow a}p(x) = p(a)$$then, for example, your left hand limit is$$ \lim_{x\rightarrow 2^-}2x+1 =2\cdot 2 + 1=5$$Similarly for the right hand limit. If they come out equal, that would give the two sided limit, otherwise it doesn't exist. [/QUOTE]
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Left and Right Hand limit of a Piece wise function?
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