I have got a problem like this :
Let f : R -> R be a function such that there exists constants b, m > 0 and c belongs to R such that
f(x) > mx + c for all x > b
using only the definition of the limit we have to prove that limit of f(x) when x goes to inifinity = inifinity
I have tried to prove it like this :
For all N > 0 if we can find some 'a' > 0 such that x > a implies (mx + c) > N
then that in turn implies f(x) > N
So that we can say limit of f(x) when x goes to inifinity = inifinity
But the problem is I can't find an 'a' > 0 for this.
I have tried to write it in reverse to find an 'a'
i.e mx + c > N
x > (N-c)/m
But here I get stuck coz 'c' can be either >= N or <N
So, can somebody please help me with this ?
What I need to do is a rigorous proof.