Question

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

Answer 1

constant

Answer 2

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

Answer 3

$$f(x) = c $$

Answer 4

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

Answer 5

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

Answer 6

I don't think so

Answer 7

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

Answer 8

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

Answer 9

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.

Answer 10

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

Answer 11

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.