Suppose that |f(x) - f(y)| \leq |x - y|n
for n > 1
Prove that f is constant by considering f '
f'(a) = limit as x->a [f(x) - f(a)]/[x-a]
The Attempt at a Solution
I'm really not sure how the derivative of "f" is going to show that...
Suppose that "f" satisfies "f(x+y)=f(x)+f(y)", and that "f" is continuous at 0. Prove that "f" is continuous at a for all a.
In class we were given 3 main ways to solve continuity proofs.
A function "f" is continuous at x=a if:
Limit of f(x) as...
Prove that the limit as x->inifinity [x^2 - 2x] / [x^3 - 5] = 0
The general procedure that we have to use to come up with this proof is:
"For all epsilon>0, there exists some N>0, such that for all x, if x>N then this implies that
| [[x^2 -...
Let a rep. any real number greater than 0
Prove that the limit as x->a of sqrt(x) = sqrt(a)
I hav to prove the above equation using using an Epsilon-Delta proof but im not sure how to start it off.
2. The attempt at a solution
I assumed that if 0<|x-a|<d
then |f(x) -...