Homework 2, due on Wednesday, April 15 by 11:59pm PST

• Chapter 4 (4.1, 4.2, 4.3, 4.4)
• Chapter 5 (5.1, 5.4, 5.6)
• Problems I on p. 53-57 (11, 15[prove your answer], 17, 18, 20)
• Recall Rolle's Theorem: If \(f(x)\) is a function which is continuous on \([a,b]\), differentiable on \((a,b)\), and \(f(a)=f(b)\), then there exists some \(c\) in \((a,b)\) such that \(f'(c)=0\).
  \(f(x)=\sin{x}-2x\) has at least one real root. Use Rolle's Theorem to show that \(f\) does not have more than one real root.
• An integer \(n\) greater than 1 is prime if the only positive integers that divide \(n\) are 1 and n. Prove that every integer greater than 1 is prime or a product of primes.