Real & Complex Analysis: Chapter 3 Exercises Requested

[benorin]

EDIT:request filled

EDIT:got it.

Can someone please post the exercises for Chapter 3 of Real and Complex Analysis by W. Rudin, 3rd edition. I have checked-out the 2 edition from the library, but our class uses the 3rd ed. and, the exercise #'s don't match between the two editions (and hence posting even a correspondence of their numberings would suffice).
I have a final on tue, Dec. 6 and I still need to complete HW for that chapter.
Thanks in advance,
-Ben

 

[lippyka]

Exercises 3.1:1. Prove that if f is a continuous real-valued function defined on an interval I, and if ε > 0, then there exists a δ > 0 such that |f(x) − f(y)| < ε for all x, y ∈ I with |x − y| < δ.2. Let f be a real-valued function defined on an interval I. Prove that if f is continuous at every point of I, then f is uniformly continuous on I.3. Let f be a real-valued function defined on an interval I. Prove that if f is continuous on I, and if the set of discontinuities of f is finite, then f is uniformly continuous on I.4. Prove that a continuous real-valued function defined on a compact interval is bounded and attains its bounds.Exercises 3.2:1. Prove that if f is a real-valued function defined on an interval I, and if f is differentiable at a point c ∈ I, then f is continuous at c.2. Let f be a real-valued function defined on an interval I, and let c ∈ I. Prove that if f is continuous at c and differentiable at every point of I \ {c}, then f is differentiable at c.3. Let f be a real-valued function defined on an interval I, and let c ∈ I. Prove that if f is continuous at c and has a finite right derivative at c, then f is differentiable at c.4. Let f be a real-valued function defined on an interval I. Prove that if f is differentiable at every point of I, then f is continuous at every point of I.