Có 20+ tài liệu thuộc chủ đề "khóa học tính toán"
tailieu.vn Xem trực tuyến Tải xuống
conditional, 953 explanation of, 952–953 implies convergence Absolute maximum point, 347 Absolute maximum value, 252, 347 Absolute minimum point, 347 Absolute minimum value, 347, 352 Absolute value function. explanation of, 61–62. due to force of gravity, 150n, 406–407 explanation of, 76. error estimate, 954–955 explanation of, 953. definition of, 603 modifications to, 604, 606 Ancient Egyptians, 95, 97n, 627, 854...
tailieu.vn Xem trực tuyến Tải xuống
An Integrated Approach to Functions and Their Rates of Change. Calculus: an integrated approach to functions and their rates of change / by Robin Gottlieb.—Preliminary ed.. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without the prior written permission of...
tailieu.vn Xem trực tuyến Tải xuống
To the Student. The art of questioning, coupled with some good, all-purpose problem-solving skills, may be more important than any neatly packaged set of facts you have tucked under your arm as you stroll away from your studies at the end of the year. But because you will want to carry away something you can use for reference in the...
tailieu.vn Xem trực tuyến Tải xuống
Functions Are Lurking Everywhere. The child learns that the position of a switch determines whether a lamp is on or off, and that the position of a faucet determines the flow of water into a sink.. The deterministic relationship between the piano key hit and the resulting note is characteristic of the input-output relationship that is the object of our...
tailieu.vn Xem trực tuyến Tải xuống
(a) Which of the following maps are maps of functions?. Which of the functions in Problem 3 are 1-to-1?. 6 Number theorists (mathematicians who study the theory and properties of numbers) are interested in the distribution of prime numbers. (a) What are you interested in studying in the future, both in terms of math and otherwise?. (b) Are there things...
tailieu.vn Xem trực tuyến Tải xuống
The height is proportional to the volume. We can see this from the function formula, h = C b (V. The walls of the beaker are perpendicular to the base. therefore all cross-sections are equal in area and the height is proportional to the volume.. In the examples that follow we will work on expressing one variable as a function...
tailieu.vn Xem trực tuyến Tải xuống
EXERCISE 1.3 Two of the four graphs given in Figure 18 are the graphs of functions. Can you come up with a rule for determining whether or not a given graph is the graph of a function?. The test for a function is that every input must have only one output assigned to it. graphically, this means if we draw...
tailieu.vn Xem trực tuyến Tải xuống
Assuming they maintain their speeds and directions, express the distance between the sisters as a function of the number of minutes since they parted.. (a) Express the volume of the cylinder as a function of its radius, r.. (b) Express the surface area of the cylinder as a function of its radius, r.. The height of a right circular cone...
tailieu.vn Xem trực tuyến Tải xuống
Which of the following functions is continuous at x = 2?. Which of the following functions is continuous at x = 1?. Every point that lies on the graph of the equation satisfies the equation. Conversely, every point whose coordinates satisfy the equation lies on the graph of the equation. The function f is the identity function. The function g...
tailieu.vn Xem trực tuyến Tải xuống
Answer parts (a), (b), and (c) for each of the trips corresponding to graphs I, II, III, and IV.. If you disagree about an answer, each of you should discuss your reasoning and see if you can come to a consensus on the answers.. What characteristic of the graph of position versus time determines the sign of the velocity?. 92...
tailieu.vn Xem trực tuyến Tải xuống
3.1 COMBINING OUTPUTS: ADDITION, SUBTRACTION, MULTIPLICATION, AND DIVISION OF FUNCTIONS. The sum, difference, product, and quotient of functions are the new functions defined respectively by the addition, subtraction, multiplication, and division of the outputs or values of the original functions.. Addition and Subtraction of Functions. EXAMPLE 3.1 Suppose a company produces widgets. 1 The revenue (money) the company takes in...
tailieu.vn Xem trực tuyến Tải xuống
(Use any means at your disposal.) (b) Find j (x. In part (a) the input of f is increased by 1. What is the effect on the graph?. In part (b) the output of f is increased by 1. In part (a) the input of f is increased by 2. In part (b) the output of f is increased by...
tailieu.vn Xem trực tuyến Tải xuống
Later in this text, when we are looking for the rate of change of a composite function, we will use the same approach of decomposition to decompose the function and find its rate of change from our knowledge of the rates of change of these simpler functions. For each of the functions given below, give possible formulas for f (x)...
tailieu.vn Xem trực tuyến Tải xuống
Your calculator probably won’t indicate the pinhole in the graph.. The zeros of the function f (x) are at x. Find the zeros of the following functions. The graph of y = f (x) is symmetric about the y-axis. Which of the following functions is equal to f (x)?. Below is the graph of y = 2 x . Using...
tailieu.vn Xem trực tuyến Tải xuống
change of − 1 minute/day. As we can see by looking at the graph in Figure 4.2, over small enough intervals, the data points either lie on a line or lie close to some line that can be fitted to the data. However, the line that fits the data best varies with the interval chosen. When looked at over the...
tailieu.vn Xem trực tuyến Tải xuống
A, B , C, D, and E are points on the graph of f . (b) What is the slope of L 1 ? (c) What is the equation of L 1. (e) What is the length of the line segment joining points B and D?. (f ) What is the slope of L 2 ? (g) What is the...
tailieu.vn Xem trực tuyến Tải xuống
6 this model correctly counts the $5 commission for the first six items in with the base rate, but then it gives an additional $25 for each of those first six items. This amounts to giving a $30 commission for each of the first six items sold. ($25/item)(7 items) instead of the correct. The slope of C(x) corresponds to the...
tailieu.vn Xem trực tuyến Tải xuống
The rock hits the ground in 4 seconds. What is its average velocity in the first second? In each consecutive second? Recall that the average velocity is given by. average velocity in the 1st second = s t = s(1) 1. 16 ft/sec average velocity in the 2nd second = s t = s(2) 2. 48 ft/sec average velocity in...
tailieu.vn Xem trực tuyến Tải xuống
Therefore the slope of the tangent line is 10/27. the equation of the tangent line is of the form y − y x − x 1. The tangent line goes through the point. Alternatively, the equation of the tangent line can be written. The limiting process enables us to get a handle on the slope of a curve and the...
tailieu.vn Xem trực tuyến Tải xuống
0 the graph of f has a horizontal tangent line.. Figure 5.15. Conclude that the derivative of x 2 + 3x is the sum of the derivatives of x 2 and 3x.. It is designed for your second reading of the chapter.. This means getting rid of the square roots. 192 CHAPTER 5 The Derivative Function. So the derivative of...