For two- and three-dimensional vectors, the fundamental property of dot products, A B = |A||B| cos , implies that |A B||A||B|. (2.3.44) In this exercise, we generalize this to n-dimensional vectors and functions, in which case (2.3.44) is known as Schwarzs inequality. [The names of Cauchy and Buniakovsky are also associated with (2.3.44).] (a) Show that |A B| 2 > 0 implies (2.3.44), where = A B/B B. (b) Express the inequality using both A B = n=1 anbn = n=1 ancn bn cn . *(c) Generalize (2.3.44) to functions. [Hint: Let A B mean the integral L 0 A(x)B(x) dx.]

Week 1 and 2 of College Pre-algebra Life Saver notes! Order of operations Remember GEMDAS 1.G rouping 2.E xponents 3.M ultiply 4.D ivide 5.A dd 6.S ubtract NOTE: when multiplying, dividing, adding, and subtracting you do it as you are reading a book; you go left to right. Important things to remember!: When there are parenthesis ( ) inside of brackets [ ] be sure to...