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anonymous

  • 5 years ago

is the limit of a constant as x--> infinity 0?

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  1. anonymous
    • 5 years ago
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    constant

  2. anonymous
    • 5 years ago
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    $$(\forall \epsilon>0)(\exists \delta>0)\rightarrow \left| f(x) - c \right|<\epsilon$$

  3. anonymous
    • 5 years ago
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    $$f(x) = c $$

  4. anonymous
    • 5 years ago
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    $$\left| c-c \right|=0<\epsilon, 0<\delta<\epsilon$$

  5. anonymous
    • 5 years ago
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    well that proved it if you're going to zero, my bad

  6. anonymous
    • 5 years ago
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    I don't think so

  7. anonymous
    • 5 years ago
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    you don't think so what? That proves it for any finite x. The infinite proof is slightly different

  8. anonymous
    • 5 years ago
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    constant is constant always it will not change anymore regarding a change of anything change in climate doesnot change the position of a tree. it is constant. so limit of a constant is constant always not zero

  9. anonymous
    • 5 years ago
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    noufal i don't think you understand delta-epsilon proofs, with the wording of your response. And the limit of a constant is zero if the constant is zero.

  10. anonymous
    • 5 years ago
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    The limit of a constant as x approaches infinity is that constant. This can be shown using delta-epsilon.

  11. anonymous
    • 5 years ago
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    which is what i proved above for finite x. The infinite proof is: \[(\forall \epsilon>0)(\exists N>0)(\forall x>N)(\left| f(x)-L \right|<\epsilon)\] f(x) = C and L = C, so \[\left| f(x)-L \right|=\left| C-C \right|=0<\epsilon\] so any x>N may be chosen to satisfy the proof.

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