is the limit of a constant as x--> infinity 0?
$$(\forall \epsilon>0)(\exists \delta>0)\rightarrow \left| f(x) - c \right|<\epsilon$$
$$f(x) = c $$
$$\left| c-c \right|=0<\epsilon, 0<\delta<\epsilon$$
well that proved it if you're going to zero, my bad
I don't think so
you don't think so what? That proves it for any finite x. The infinite proof is slightly different
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
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.
The limit of a constant as x approaches infinity is that constant. This can be shown using delta-epsilon.
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.
Join our real-time social learning platform and learn together with your friends!