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1. ### Derivative proof

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...
2. ### Continuity Proof

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...
3. ### Limit Proof

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 -...
4. ### Epsilon-Delta Proof

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) -...