I consider the problems assigned from the book to be routine practice problems. You should be able to do all of these, though some may take a little thought. I will mark the harder ones on the assignments with an asterisk. If you find that you are having trouble doing many of the book problems, you should ask questions about them in class or come to my office hours.
Answers to most odd-numbered problems are in the back of the book. I also will assign some even numbered problems; you should not feel that you must confirm your answer with an authority in order to feel confident in your result. In life there is no back of the book, so you need to gain practice feeling confident in your own work. If you don't feel sure of your result, try some of the other odd-numbered problems near it in the book until you feel more confident. If you are still not sure, perhaps you need to look at your notes or the chapter in the book some more. If you understand the material, you should know that you do, and not doubt your result.
You should do all the problems, not just the first few. The harder ones usually are toward the end of the assignment, and these are the more important ones to do. Also, pay special attention to any problems that are not from the book, as these represent ideas that are important enough to me to take the time to write them out. These are where you will get your best practice with the material.
Mathematics is a discipline than can only be learned by doing. Listening to a lecture is not the same thing as working through problems on your own, so if you plan to learn the material, you really must do at least the assigned problems.
See the study suggestions for some helpful hints on homework.