tailieunhanh - Calculus: An Integrated Approach to Functions and their Rates of Change, Preliminary Edition Part 4

Calculus: An Integrated Approach to Functions and their Rates of Change, Preliminary Edition Part 4. A major complaint of professors teaching calculus is that students don't have the appropriate background to work through the calculus course successfully. This text is targeted directly at this underprepared audience. This is a single-variable (2-semester) calculus text that incorporates a conceptual re-introduction to key precalculus ideas throughout the exposition as appropriate. This is the ideal resource for those schools dealing with poorly prepared students or for schools introducing a slower paced, integrated precalculus/calculus course | What Are Functions Basic Vocabulary and Notation 11 g The rule assigns to every number the square of that number. h The rule assigns to every nonzero number the reciprocal of that number. 3. a Which of the following maps are maps of functions I a b c c d e II a------ a b------ b c ----- x d------ d e ----- z III a a b b--- b c c d IV a b c d e b For each function determine the range and the domain. 4. Which of the functions in Problem 3 are 1-to-1 5. There are infinitely many prime numbers. This has been known for a long time Euclid proved it sometime between 300 . and 200 Number theorists mathematicians who study the theory and properties of numbers are interested in the distribution of prime numbers. Let P n number of primes less than or equal to n where n is a positive number. Is P n a function Explain. 6. Writing We would like to tailor this course to your needs and interests therefore we d like to find out more about what these needs and interests are. On a sheet of paper separate from the rest of your homework please write a paragraph or two telling us a bit about yourself by addressing the following questions. a What are you interested in studying in the future both in terms of math and otherwise b Are there things you have found difficult or confusing in mathematics in the past If so what c What was your approach to studying mathematics in the past Did it work well for you d What are your major extracurricular activities or interests e What do you hope to get out of this course For Problems 7 through 9 determine whether the relationship described is a function. If the relationship is a function a what is the domain the range b is the function 1-to-1 6The proof went like this Assume there are finitely many primes 2 3 5 7 . N where N is the largest prime. Let M 2 - 3 - 5 - 7 - . . . N 1 . let M be 1 bigger than the product of all the primes. Then M is not divisible by any of the primes on the list. But that means the list doesn t include all .