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# Class Note for MATH 1314 with Professor Gross at UH 2

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This 5 page Class Notes was uploaded by an elite notetaker on Friday February 6, 2015. The Class Notes belongs to a course at University of Houston taught by a professor in Fall. Since its upload, it has received 14 views.

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Date Created: 02/06/15
M1314 lesson 22 1 Math 1314 Lesson 22 Functions of Several Variables So far we have looked at functions of a single variable In this section we will consider functions of more than one variable You are already familiar with some examples of these Pxy 2x 2y AP it P1 it These formulas are functions of several variables We have just never called them that before We will for the most part limit our discussion to functions of two variables Functions of Two Variables Definition A real valued function of two variables f consists of a set A of ordered pairs of real numbers x y called the domain of the function and a rule that associates with each ordered pair in the domain of f one and only one real numb r denoted by zfxy t 4 X 2 D OVYVI You will need to learn several skills using functions of several variables 1 Evaluating a function of several variables at a given point Example 1 Suppose fx y 3x2y 4xy6 Compute f00f2 1 and f 1 3 x L5 2 Mom 30ICovo0olCop Comm 42 3 sczv C D qmc m a T zzggz C27l7 4G 3 3 3 074qu 0633 Cl lZ 91 quotlS Thai ls M1314 lesson 22 2 Example 2 The volume of a cylindrical tank with radius r and height h is given by the formula Find the volume of a tank with m and m feet liw rm 71 0200317200 3 13 ZZpl l393 it Example 3 Suppose you borrow money to buy a house You Suppose you borrowed 0000 at 6 an I interest How much has the balanc the loan gone down a making 60 payments How much is the remaining balance of t n after 20 years of payments M1314 lesson 22 3 2 Find the domain of a function of several variables We ll have several kinds of situations that are similar to finding domain of functions of a single variable Problems arise when we have rational functions functions involving radicals and logarithmic functions Example 4 Find the domain of the function fx y 2x2 3y2 PCth omlal gt QOMQ M is all real numbers 3x 2x 5y 39 Example 5 Find the domain of the function fx y g X S 9 O 02x 392 5 2 i 5 X 3 Or X j Z 3 l lS dQFnleol gor all Yea hUxmers QQPJL UJl RK b ngt or X2733 M1314 lesson 22 4 Example 6 Find the domain of the function fXym eaoi lb39XLDQZO 7 up 2 gtlt1jz 0r 7lt alillp Tlac domain 0 ls a dee 0 radius d located oc u Origin Oil16K fiducka all the BQCAQS Graphing functions in space is quite difficult You will not need to do this Here are a couple of examples of graphs of functions of two variables W039o o M kw I 95 o l 9 W O mu ismw Hopefully you ll recognize how difficult it would be to graph these manually We usually graph function of two variables using a computer M1314 lesson 22 Here s an example of graphing just one point in space Example 7 Graph the point 2 3 5 From this section you should be able to Evaluate a function of several variables Find the domain of a function of several variables

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