Primer Assignment for Mathematics 1b Problem Set 0 This problem set is due Thursday February 12 or Friday February 13 depending upon whether you are in a MWF or a TTH class There will be help available for those who need it See the course website under News for details Part I Primer for Integration The first third of this course deals with integration and its applications This part of the problem set is designed to be a primer You are expected to know the integrals in problem 1 If you don t review section 5 3 in Stewart to learn them 1 Evaluate the following R a un du n 6 1 R b u1 du R c sin u du R d cos u du R e sec2 u du R f eu du R g bu du R 1 h 1 u 2 du R 1 i 1 u2 du 2 Knowing the integrals from problem 1 do the integrals below by substitution If you need review look at section 5 5 in Stewart R 1 R R 1 iii a i 2x 1 3 dx ii 2x 1 3 dx 2x 1 dx R R 2 R R b i x x2 5 dx cos x sin x dx iii t sin t3 dt iv tan t dt ii R ex R x R ln x dx ii iii c i x dx e x dx ex2 3 To prime yourself for applications read Stewart section 5 2 and on page 438 from the Concept Check do 2 and 5 Part II Graphing Primer Learning Goal There are many different ways to look at mathematical problems often a graphical approach is fruitful In order to use this approach successfully you need familiarilty with the graphs of some basic functions For example in addition to being able to graph lines and parabolas you should have some expectations about what the graphs of higher order polynomials can look like This will be important for understanding Taylor and MacLaurin series You should be able to draw the graphs of trigonometric functions such as sin x cos x and tan x of exponential functions such as ex and e x and of the logarithmic function This is by no means an exhaustive list of all the functions you may run into in your studies but it is a beginning Some of you may have become accustomed to leaning very heavily on a graphing calculators for anything having to do with graphing The exercises that follow are meant to prime your graphing skills You should use a graphing calculator or the graphing capacity of a computer to check your work but not to do it 1 How are the graphs of y f x and y f x 2 related If the zeros roots of f x are at x 3 7 and 10 what are the zeros of f x 2 2 What are characteristics of polynomials that distinguish them from exponential trigonometric and logarithmic functions 1 3 Look at the graphs on the bottom of the next page Write a possible formula for each function There may be more than one correct answer to some of these problems Check your answer with a graphing calculator or a computer The domain of the function in graph III is x x 1 all other functions have the domain The functions graphed in IV and V are periodic The function graphed in VII has infinitely many zeros and the zeroes are equally spaced Hints Two of the functions are basically trigonometric two are basically exponential functions one is a polynomial one is a logarithmic funtion and one requires multiplication of different varieties of functions The answers to some of these problems are not unique f x f x 3 2 3 I x 3 II f x x f x x 1 2 III IV f x 2 x 2 f x 1 x V 2 f x 1 1 x 2 VI x VII 2