Lecture 7: Creating New Functions Binomial Theorem

Assignment

By today you should have read through section 2.2 of the text and done problems 3,9,11,25,43-47,63 in section 2.1 and
problems 21-23,27-29, 37-41, 47, 53 in section 2.2.

Brief review of the lecture

We talked about how to add functions. In fact we can combine two given functions using any of the four arithmetic operations, +, -, x, / as long as we are careful to realize that the domains may be different from the two combined functions. When a symbolic representation of a function is given but no domain is specified, we assume the domain is the set of all x values for which the formula results in a real number. for example F(x)= x/(x-2) has domain all real numbers except 2, unless the domain is provided to the reader. The most important methos of creating new functions from old functions is the process of composition. Much of our time will be spent understanding this process. It is important to be able to both compose functions and to decompose them. The most important rule of differentiation, called the CHAIN Rule, depends on the users ability to break down complicated functions into compositions of simpler ones.

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