I'm currently in a class that uses Spivak's Calculus. Because of (fairly) good explanations and proofs, fun and challenging exercises, and some witty comments he gives occasionally, I really enjoy using this book. The only problem I find, however, is that sometimes I spend far too long on some problems - which means that I'm not able to cover all problems before a test/exam. Strictly in interest of time, is it justified to use the solution manual to go over the solutions to SOME problems (and then reproduce the proofs myself without looking again), or should I work hard on each and every problem that I have the time for (knowing that doing this probably won't allow me to finish all)? Which one is better for gaining mastery of the content?
This is definitely a question many students face, and has been discussed a bit on this site as well (see this excellent answer). In general, I think it's unwise to try and study and completely understand/come up with a solution to each and every exercise in a book. You should definitely read the solution after struggling for a while (~$1$h) and (re)reading the text, thinking about the exercises. But there might be literally thousands of exercises, and it would take significant effort to come up with all their solutions yourself, hence I think you should not attempt every question, and even in those you do, give up after a while if you cannot solve them. Instead, in textbooks which explicitly mark difficulty level, I would recommend trying $5$ or so from the "basic" questions per section/chapter to make sure you get the basics, $2$ to $3$ from the middle-level question, and $1$ question from the most difficult level. You should see the linked answer for more in depth discussion.