Recent content by clarence829

Everything just finally clicked and it all makes sense now. Thanks again for the help.

@SammyS I see how you're getting your solution and I appreciate the help. After the question in my textbook (Lang) it says "Hint: Write x=x+y-y, and apply |a+b| ≤ |a|+|b|, together with the fact that |-y|=|y|. How would one use x=x+y-y in solving this proof?

If I could get to |x+y|+|-y|≥ |x| then I'd just have to pull |-y| to the right side of the inequality and apply |-y|=|y| to |-y| and I'd have my proof. The problem is that I'm unfamiliar with the various algebraic rules that apply to absolute value, particularly in inequalities. What are the...

Homework Statement Prove the following inequalities for all numbers x, y. |x+y| ≥ |x|-|y| [Hint: Write , and apply , together with the fact that Homework Equations These were given as hints in my textbook: x=x+y-y |a+b| ≤ |a| + |b| |-y|=|y| The Attempt at a Solution...

One of my friend's has Stewart's Calculus. Should I save the money and use his textbook or is it worth the money to track down a used copy of Lang's?

Thank you both for the responses. Two follow up questions for micromass: 1) Do you think the trigonometry I learned in high-school precalculus will be sufficient to work my way through Lang's Calculus I? 2) Is Spivak's Calculus actually Calculus II?

I'm interested in teaching myself the following subjects: - Calculus I, II, and III - Linear Algebra - Differential equations The highest math courses I've taken are pre-calculus in high school and business calculus in high school. What books would you all recommend for learning...