# Homework Help: Advanced Calculus Fitzpatrick 2e

1. Aug 26, 2008

### propensity

If anyone of you got the book Advanced Calculus 2e by Fitzpatrick I would appreciate your posting of the questions 14, 15, 16 on page 20. My order of the book hasn't reached me but I need to turn in the homework tomorrow. I just need the questions.

Thank you.

2. Aug 26, 2008

### konthelion

Here are the questions:

14.(Cauchy’s Inequality) Using the fact that the square of a real number is nonnegative, prove that for any numbers a and b
Prove that:
$$ab \leq \frac{1}{2} \left( a^2+b^2)$$

15. Use Cauchy's Inequality to prove that if $$a \geq 0$$ and $$b \geq 0$$ , then
$$\sqrt{ab} \leq \frac{1}{2} \left( a + b \right)$$

16. use Cauchy's Inequality to prove for any numbers a and b and a natural number n

$$ab \leq \frac{1}{2} \left( na^2 + \frac{1}{n}b^2 \right)$$

This is why you should buy your books at the bookstore for the beginning of classes(in case professors assign homework problems), even if you pre-order then online. You can always return them for a refund.

3. Aug 26, 2008

### Dick

Wow, this is a first. I don't think I've seen anyone ask for a question rather than an answer. Good job rising to the occasion konthelion! And good advice.

4. Aug 26, 2008