Nature of Mathematics (MindTap Course List)
13th Edition
ISBN: 9781133947257
Author: karl J. smith
Publisher: Cengage Learning
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Textbook Question
Chapter 1.3, Problem 29PS
Level 1
In problems 25-30, first estimate your answer and then calculate the exact answer.
In the musical Rent, there is a song called “Seasons of Love” that uses the number 525, 600 minutes. How long is this?
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(b) Find the (instantaneous) rate of change of y at x = 5.
In the previous part, we found the average rate of change for several intervals of decreasing size starting at x = 5. The instantaneous rate of
change of fat x = 5 is the limit of the average rate of change over the interval [x, x + h] as h approaches 0. This is given by the derivative in the
following limit.
lim
h→0
-
f(x + h) − f(x)
h
The first step to find this limit is to compute f(x + h). Recall that this means replacing the input variable x with the expression x + h in the rule
defining f.
f(x + h) = (x + h)² - 5(x+ h)
=
2xh+h2_
x² + 2xh + h² 5✔
-
5
)x - 5h
Step 4
-
The second step for finding the derivative of fat x is to find the difference f(x + h) − f(x).
-
f(x + h) f(x) =
= (x²
x² + 2xh + h² -
])-
=
2x
+ h² - 5h
])x-5h) - (x² - 5x)
=
]) (2x + h - 5)
Macbook Pro
Evaluate the integral using integration by parts.
Sx² cos
(9x) dx
Let f be defined as follows.
y = f(x) = x² - 5x
(a) Find the average rate of change of y with respect to x in the following intervals.
from x = 4 to x = 5
from x = 4 to x = 4.5
from x = 4 to x = 4.1
(b) Find the (instantaneous) rate of change of y at x = 4.
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Chapter 1 Solutions
Nature of Mathematics (MindTap Course List)
Ch. 1.1 - IN YOUR OWN WORDS In the text, it was stated that...Ch. 1.1 - IN YOUR OWN WORDS What do you think the primary...Ch. 1.1 - Prob. 3PSCh. 1.1 - Prob. 4PSCh. 1.1 - IN YOUR OWN WORDS In Example 1, we concluded that...Ch. 1.1 - Prob. 6PSCh. 1.1 - Describe the location of the numbers 1, 2,3, 4,5,...Ch. 1.1 - Describe the location of the numbers 1,4,10,20,35,...Ch. 1.1 - a.If family has 5 children, in how many ways could...Ch. 1.1 - a. If a family has 7 children, in how many ways...
Ch. 1.1 - In Problems 11-14, what is the number of direct...Ch. 1.1 - In Problems 11-14, what is the number of direct...Ch. 1.1 - In Problems 11-14, what is the number of direct...Ch. 1.1 - In Problems 1114, what is the number of direct...Ch. 1.1 - Use the map in Figure 1.6 to determine the number...Ch. 1.1 - Prob. 16PSCh. 1.1 - Prob. 17PSCh. 1.1 - Prob. 18PSCh. 1.1 - A car pulls onto the USS Nimitz, which is now a...Ch. 1.1 - The ferry portion on the USS Nimitz, houses 10...Ch. 1.1 - Ten full crates of walnuts weith 410 pounds,...Ch. 1.1 - There are three separate, equal-size boxes, and...Ch. 1.1 - Prob. 23PSCh. 1.1 - Prob. 24PSCh. 1.1 - a. What is the sum of the numbers in row 1 of...Ch. 1.1 - What is the sum of the numbers in row n of Pascals...Ch. 1.1 - Use the map in Figure 1.6 to determine the number...Ch. 1.1 - Prob. 28PSCh. 1.1 - Prob. 29PSCh. 1.1 - Use the map in Figure 1.6 to determine the number...Ch. 1.1 - Problems 31-44 are not typical math problems but...Ch. 1.1 - Problems 31-44 are not typical math problems but...Ch. 1.1 - Problems 31-44 are not typical math problems but...Ch. 1.1 - Problems 31-44 are not typical math problems but...Ch. 1.1 - Prob. 35PSCh. 1.1 - Prob. 36PSCh. 1.1 - Prob. 37PSCh. 1.1 - Prob. 38PSCh. 1.1 - Problems 31-44 are not typical math problems but...Ch. 1.1 - Prob. 40PSCh. 1.1 - Prob. 41PSCh. 1.1 - Problems 31-44 are not typical math problems but...Ch. 1.1 - Problems 31-44 are not typical math problems but...Ch. 1.1 - Prob. 44PSCh. 1.1 - Prob. 45PSCh. 1.1 - Prob. 46PSCh. 1.1 - Prob. 47PSCh. 1.1 - Prob. 48PSCh. 1.1 - A boy cyclist and a girl cyclist are 10 miles...Ch. 1.1 - Prob. 50PSCh. 1.1 - Alex, Beverly, and Cal live on the same straight...Ch. 1.1 - In a different language, liro cas means red...Ch. 1.1 - Prob. 53PSCh. 1.1 - Prob. 54PSCh. 1.1 - Prob. 55PSCh. 1.1 - The number 6 has four divisorsnamely, 1,2,3, and...Ch. 1.1 - Consider the routes from A to B and notice that...Ch. 1.1 - HISTORICAL QUEST Thoth, an ancient Egyptian god of...Ch. 1.1 - A magician divides a deck of cards into two equal...Ch. 1.1 - Prob. 60PSCh. 1.2 - IN YOUR OWN WORDS Discuss the nature of inductive...Ch. 1.2 - IN YOUR OWN WORDS Explain what is meant by the...Ch. 1.2 - IN YOUR OWN WORDS What do you mean by order of...Ch. 1.2 - IN YOUR OWN WORDS What is the scientific method?Ch. 1.2 - IN YOUR OWN WORDS Explain inductive reasoning....Ch. 1.2 - IN YOUR OWN WORDS Explain deductive reasoning....Ch. 1.2 - Perform the operations in Problems 7-18. a. 5+26...Ch. 1.2 - Perform the operations in Problems 7-18. a. 14+63...Ch. 1.2 - Perform the operations in Problems 7-18. a. 38+37...Ch. 1.2 - Perform the operations in Problems 7-18. a. (8+6)2...Ch. 1.2 - Prob. 11PSCh. 1.2 - Prob. 12PSCh. 1.2 - Prob. 13PSCh. 1.2 - Prob. 14PSCh. 1.2 - Prob. 15PSCh. 1.2 - Prob. 16PSCh. 1.2 - Prob. 17PSCh. 1.2 - Perform the operations in Problems 7-18. a....Ch. 1.2 - Does the B.C. cartoon illustrate inductive or...Ch. 1.2 - Does the news clip below illustrate inductive or...Ch. 1.2 - Problems 21-24 are modelled after Example 1. Find...Ch. 1.2 - Problems 21-24 are modelled after Example 1. Find...Ch. 1.2 - Problems 21-24 are modelled after Example 1. Find...Ch. 1.2 - Problems 21-24 are modelled after Example 1. Find...Ch. 1.2 - a. What is the sum of the first 25 consecutive odd...Ch. 1.2 - a. What is the sum of the first 50 consecutive odd...Ch. 1.2 - The first known example of a magic square comes...Ch. 1.2 - HISTORICAL QUEST The Lo-shu magic square in...Ch. 1.2 - Consider the square shown in Figure 1.11. 10 7 8...Ch. 1.2 - Prob. 30PSCh. 1.2 - HISTORICAL QUEST Magic squares remind us of Sudoku...Ch. 1.2 - HISTORICAL QUEST Magic squares remind us of Sudoku...Ch. 1.2 - Prob. 33PSCh. 1.2 - Prob. 34PSCh. 1.2 - Use Euler circles to check the validity of the...Ch. 1.2 - Use Euler circles to check the validity of the...Ch. 1.2 - Prob. 37PSCh. 1.2 - Use Euler circles to check the validity of the...Ch. 1.2 - Use Euler circles to check the validity of the...Ch. 1.2 - Use Euler circles to check the validity of the...Ch. 1.2 - Use Euler circles to check the validity of the...Ch. 1.2 - Use Euler circles to check the validity of the...Ch. 1.2 - Prob. 43PSCh. 1.2 - Prob. 44PSCh. 1.2 - Prob. 45PSCh. 1.2 - Prob. 46PSCh. 1.2 - Prob. 47PSCh. 1.2 - Prob. 48PSCh. 1.2 - Which direction is the bus travelling? Did you...Ch. 1.2 - Prob. 50PSCh. 1.2 - Consider the following pattern:...Ch. 1.2 - Consider the following pattern:...Ch. 1.2 - What is the sum of the digits in 3333333342. Did...Ch. 1.2 - Prob. 54PSCh. 1.2 - How many squares are there in Figure 1.11? FIGURE...Ch. 1.2 - How many triangles are there in Figure 1.12?...Ch. 1.2 - You have 9 coins, but you are told that one of the...Ch. 1.2 - Prob. 58PSCh. 1.2 - Prob. 59PSCh. 1.2 - Prob. 60PSCh. 1.3 - Level 1 IN YOUR OWN WORDS What do we mean by...Ch. 1.3 - Level 1 IN YOUR OWN WORDS Define scientific...Ch. 1.3 - Level 1 IN YOUR OWN WORDS Do you plan to use a...Ch. 1.3 - Level 1 4. IN YOUR OWN WORDS Describe differences...Ch. 1.3 - Level 1 IN YOUR OWN WORDS What is the largest...Ch. 1.3 - Level 1 IN YOUR OWN WORDS What is a trillion? Do...Ch. 1.3 - Level 1 Write each of the numbers in Problems 7-10...Ch. 1.3 - Level 1 Write each of the numbers in Problems 7-10...Ch. 1.3 - Level 1 Write each of the numbers in Problems 7-10...Ch. 1.3 - Level 1 Write each of the numbers in Problems 7-10...Ch. 1.3 - Prob. 11PSCh. 1.3 - Prob. 12PSCh. 1.3 - Prob. 13PSCh. 1.3 - Prob. 14PSCh. 1.3 - Prob. 15PSCh. 1.3 - Level 1 Write each of the numbers in Problemc15-18...Ch. 1.3 - Level 1 Write each of the numbers in Problemc15-18...Ch. 1.3 - Prob. 18PSCh. 1.3 - Prob. 19PSCh. 1.3 - Prob. 20PSCh. 1.3 - Prob. 21PSCh. 1.3 - Prob. 22PSCh. 1.3 - Prob. 23PSCh. 1.3 - Prob. 24PSCh. 1.3 - Prob. 25PSCh. 1.3 - Prob. 26PSCh. 1.3 - Prob. 27PSCh. 1.3 - Prob. 28PSCh. 1.3 - Level 1 In problems 25-30, first estimate your...Ch. 1.3 - Prob. 30PSCh. 1.3 - Prob. 31PSCh. 1.3 - Prob. 32PSCh. 1.3 - Prob. 33PSCh. 1.3 - Level 2 Compute the results in Problems 31-36....Ch. 1.3 - Prob. 35PSCh. 1.3 - Level 2 Compute the results in Problems 31-36....Ch. 1.3 - Prob. 37PSCh. 1.3 - Prob. 38PSCh. 1.3 - Prob. 39PSCh. 1.3 - Prob. 40PSCh. 1.3 - Prob. 41PSCh. 1.3 - Prob. 42PSCh. 1.3 - Prob. 43PSCh. 1.3 - Prob. 44PSCh. 1.3 - Prob. 45PSCh. 1.3 - Level 2 In Problems 41-48, you need to make some...Ch. 1.3 - Prob. 47PSCh. 1.3 - Prob. 49PSCh. 1.3 - Level 3 HISTORICAL QUEST Zerah Colburn 1804-1840...Ch. 1.3 - Prob. 51PSCh. 1.3 - Prob. 52PSCh. 1.3 - Level 3 The Library of Congress contains about 35...Ch. 1.3 - Level 3 A sheet of notebook paper is approximately...Ch. 1.3 - Prob. 55PSCh. 1.3 - Problem Solving Level 3 If it takes one second to...Ch. 1.3 - Prob. 57PSCh. 1.3 - Prob. 58PSCh. 1.3 - Prob. 59PSCh. 1.3 - Problem Solving Level 3 It is known that a persons...Ch. 1.CR - In your own words Compare and contrast the...Ch. 1.CR - IN YOUR OWN WORDS Describe Polyas problem-solving...Ch. 1.CR - Prob. 3CRCh. 1.CR - Compute 111,111,111111,111,111. Do not use direct...Ch. 1.CR - Prob. 5CRCh. 1.CR - Prob. 6CRCh. 1.CR - Prob. 7CRCh. 1.CR - Prob. 8CRCh. 1.CR - Prob. 9CRCh. 1.CR - Prob. 10CRCh. 1.CR - Prob. 11CRCh. 1.CR - Prob. 12CRCh. 1.CR - Rearrange the cards in the formation shown here so...Ch. 1.CR - Prob. 15CRCh. 1.CR - Prob. 16CRCh. 1.CR - Prob. 17CRCh. 1.CR - Prob. 18CRCh. 1.CR - Prob. 19CRCh. 1.CR - Prob. 20CR
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