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OpenStudy (blank):

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

OpenStudy (anonymous):

constant

OpenStudy (anonymous):

$$(\forall \epsilon>0)(\exists \delta>0)\rightarrow \left| f(x) - c \right|<\epsilon$$

OpenStudy (anonymous):

$$f(x) = c $$

OpenStudy (anonymous):

$$\left| c-c \right|=0<\epsilon, 0<\delta<\epsilon$$

OpenStudy (anonymous):

well that proved it if you're going to zero, my bad

OpenStudy (anonymous):

I don't think so

OpenStudy (anonymous):

you don't think so what? That proves it for any finite x. The infinite proof is slightly different

OpenStudy (anonymous):

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

OpenStudy (anonymous):

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.

OpenStudy (anonymous):

The limit of a constant as x approaches infinity is that constant. This can be shown using delta-epsilon.

OpenStudy (anonymous):

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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