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Đây là cuốn sách tiếng anh trong bộ sưu tập "Mathematics Olympiads and Problem Solving Ebooks Collection",là loại sách giải các bài toán đố,các dạng toán học, logic,tư duy toán học.Rất thích hợp cho những người đam mê toán học và suy luận logic.
[...]...This page intentionally left blank Introduction Strategies for Solving Word Problems The power of calculus lies in its ability to solve applied problems in such diverse areas as physics, chemistry, biology, business, economics, and the social sciences Invariably, human beings, using words that attempt to describe some realistic situation, pose such problems This book addresses the... solving word problems in their calculus courses The first task in solving a word problem is to develop a model for the problem at hand A mathematical model is a description of the problem in terms of variables, functions, equations, and other mathematical entities Once it has been modeled, the second task is to solve the problem using the appropriate mathematical tools Setting up and solving a calculus. .. viewing the solution of a problem and solving the problem by yourself When you read an example in this book, you may be able to follow every step but you should not be misled into thinking that you completely understand the solution Learning to solve problems is like learning to play a musical instrument You may think a musical selection is simple while watching your teacher play it with ease, but it... guidelines described in this book, you will master this all-important skill xii Chapter 1 Extracting Functions from Word Problems Calculus is the study of the behavior of functions The ability to solve “real life” problems using calculus hinges upon the ability to extract a function from a given description or physical situation Students usually find that a word problem is easily solved once the underlying... is to learn xi Copyright 2001 The McGraw-Hill Companies Click Here for Terms of Use general procedures, which can be applied to all problems within a specific category Reading a word problem is not like reading a novel Every word is important and must be clearly understood if you are to successfully arrive at the solution Feel free to use a dictionary, if necessary, to clarify the meaning of seemingly... function is determined In this chapter we discuss techniques that will form the basis for solving a variety of word problems encountered in calculus courses One definition of a function found in calculus texts reads: A function is a rule that assigns to each number x ε A, a unique number y ε B In calculus, A and B are sets of real numbers A is called the domain and B the range It is important to understand... 3 To obtain a relationship between r and h we use basic geometry Viewing the problem from a two-dimensional 15 perspective, we observe two similar triangles: ABC is similar to ADE 6 D 6 2r = h 10 B E 2r 20r = 6h C 10 h 3h r = 10 A Substituting into the volume equation in step 2, we obtain π 3h V(h) = 3 10 = V(h) = 2 h π 9h2 · ·h 3 100 3π 3 h 100 Business and Economics Problems Problems arising in. .. the quantity to be expressed as a function This quantity will usually be represented in terms of two or more variables Step 3 Use any constraints specified in the problem to eliminate all but one independent variable A constraint defines a relationship between variables in the problem The procedure is not complete until only one independent variable remains 3 Number Problems Although number problems are... caused you difficulty Then cover the solution again and continue Repeat this process every time you get stuck When you finally get to the end, take a deep breath and then attempt the problem again from the beginning You have truly mastered the problem only if you can go from the beginning to the end by yourself without looking at the authors’ solution Solving word problems is more of an art than a science... of one of the numbers Solution Step 1 In most number problems a diagram is not called for We label the numbers using the variables x and y Let x be the first number y be the second number Step 2 We wish to express the product P as a function, so P = xy Step 3 Since x + y = 40, y = 40 − x We substitute into the equation involving P obtained in step 2 and express using function notation P (x) = x(40 − . Problems in Algebra How to Solve Word Problems in Arithmetic How to Solve Word Problems in Chemistry How to Solve Word Problems in Geometry How to Solve Word Problems. alt="" How to Solve Word Problems in Calculus A Solved Problem Approach TLFeBOOK Other books in the How to Solve Word Problems series: How to Solve Word Problems