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单词 limit from the left and right
释义
limit from the left and right

Mathematics
  • The statement that f(x) tends to l as x tends to a from the left can be written: f(x)→ l as xa. Another way of writing this is

    limxaf(x)=l.

    The formal definition says that this is so if, given ε‎>0, there is a number δ‎>0 such that, for all x strictly between aδ‎ and a, f(x) lies between lε‎ and l + ε‎. In place of xa, some authors use xa. In the same way, the statement that f(x) tends to l as x tends to a from the right can be written: f(x) → l as xa+. Another way of writing this is

    limxa+f(x)=l.

    The formal definition says that this is so if, given ε‎>0, there is a number δ‎>0 such that, for all x strictly between a and a + δ‎, f(x) lies between lε‎ and l + ε‎. In place of xa+, some authors use xa. For example, if f(x) = x−[x], then

    limx1f(x)=1,limx1+f(x)=0.

    limit from the left and right

    The graph of x – [x]


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