These will often give you the problem statements and answers—allowing you to reverse-engineer the concepts even if you are using a library copy.
One textbook has stood as a quiet sentinel at this crossroads: patrick m fitzpatrick advanced calculus pdf google link
The Second Edition of this text, published by the American Mathematical Society, is celebrated for its rigorous yet accessible approach to the transition from computational calculus to formal analysis. These will often give you the problem statements
Covers continuity, differentiability, integrability, and power series. published by the American Mathematical Society
: A preview of the text, including table of contents and selected chapters, is available on Google Books Library & Archive Options Internet Archive
The book starts at the very beginning, using the completeness axiom to build the real number system from the ground up.