Hmm wait a minute.
f'(x) = limit as x->y [f(x) - f(y)]/[x-y]
is the formula for the derivative.
Does this formula still hold if [f(x) - f(y)]/[x-y] is in absolute value signs?
Ok I tried doing that but I'm having trouble with the absolute value signs.
This is what I got but I'm not sure if the absolute value signs are in the right place for the LHS.
|f[x] - f[y] / x-y | is less than or equal to |x-y|^n-1
then i take limit as x->y for both sides.
Paying attention to...
Homework Statement
Suppose that |f(x) - f(y)| \leq |x - y|n
for n > 1
Prove that f is constant by considering f '
Homework Equations
Well
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...
Homework Statement
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.
Homework Equations
In class we were given 3 main ways to solve continuity proofs.
A function "f" is continuous at x=a if:
a.)
Limit of f(x) as...
Sorry spidey we had to be more rigorous in our proof.
Thanks a bunch HallsofIvy that got me thinking on the right track although it wasnt exactly in the correct method that we have to do it in.
Yes gibz we had to structure it as an epsilon-delta proof but i was able to use hallsofivys solution...
Homework Statement
Prove that the limit as x->inifinity [x^2 - 2x] / [x^3 - 5] = 0
Homework Equations
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 -...
Homework Statement
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) -...