## anonymous 5 years ago is the limit of a constant as x--> infinity 0?

1. anonymous

constant

2. anonymous

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

3. anonymous

$$f(x) = c$$

4. anonymous

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

5. anonymous

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

6. anonymous

I don't think so

7. anonymous

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

8. 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

9. 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.

10. anonymous

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

11. 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.