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# Class Note for MATH 1314 with Professor Heeth at UH

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COURSE
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PAGES
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KARMA
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This 4 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 15 views.

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Date Created: 02/06/15
Example 3 Suppose you borrow money to buy a house You agree to a 30year loan with equal payments This formula gives the amount of the reduction in principal of the loan given in dollars after making 139 payments on a loan of A dollars amortized over I years 15 4 B A t39A 5 quot 1 1121221 Suppose you borrowed 180000 at 6 annual interest How much has the balance of the loan gone down after making 60 payments How much is the remaining balance of the loan after 20 years of payments 2 Find the domain of a function of several variables We ll have several kinds of situa tions that are similar to nding 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 x y 2x2 3y2 3x 2x 5y Example 5 Find the domain of the function f x y Example 6 Find the domain ofthe function fx y 16 x2 yz 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 Hopefully you recognize how difficult it would be to graph these manually We usually graph function of two variables using a computer 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 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 Px y 2x 2y dim xa 136 2 at 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 setA 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 number denoted by z x y 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 x y 3x2y 7 4xy 6 Computef0 0f2 1 andfl 3 Example 2 The volume of a cylindrical tank with radius r and height h is given by the formula V r h nrzh Find the volume of a tank with radius 6 and height 20 feet

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