Best Limit & Calculus Books for College Students

[NooDota]

What are some good limit books, I'm looking for something that:

1. Talks about limits from A-Z, covering everything about them.
2. Has lots of limit problems and examples.
3. Mainly, I want it to have a doctrine for finding a limit, or somewhat a constant approach, like when you have 0/0 in specific function, your goal should be xyz..

College starts next year, and they only started teaching us about limits last year, my maths books are awful, they have no sets of methods or anything, and there are rules they don't allow you to use, like L'Hopital's.Also, if you know any good calculus books that explain it in a simple way, but also reaching the college level, that'd be great.

 

[Dr. Courtney]

I like Stewart, but I'm not sure you can divorce your recipe from common sense.

We used the pnemonic device DANG:

D - try direct substitution
A - try algebraic manipulation
N - Take a numberical approach, plugging in numbers closer and close from both sides
G - Try a graphical approach

You have to be flexible in your approach to limits and try something else if your first attempts fail.

 

[NooDota]

The limits I have in my book are easy, but since we have no methods, I'm having a hard time solving the hard ones. There must be some book with a set of methods or something? I'm not allowed to us graphical approaches.

For example, a limit I couldn't solve is: lim f(x)= (ln(x) - 1)/(x-e) when x approaches e.