CALCULUS WITH APPLICATIONS
11th Edition
ISBN: 2818440028625
Author: Lial
Publisher: ELSEVIER
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Chapter 11, Problem 29RE
(a)
To determine
To find: The mean.
(b)
To determine
To find: The standard deviation.
(c)
To determine
To find: The probability that the value of the random variable will be less than the mean.
(d)
To determine
To find: The probability that the value of the random variable will be within 1 standard deviation of the mean.
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MATH 122
WORKSHEET 3
February 5, 2025
. Solve the following problems on a separate sheet. Justify your answers to earn full credit.
1. Let f(x) = x² - 2x + 1.
(a) Find the slope of the graph of y = f (x) at the point P = (0,1) by directly
evaluating the limit:
f'(0) = lim (
f(Ax) - f(0)
Ax
Ax→0
(b) Find the equation of the tangent line 1 to the graph of ƒ at P.
What are the x and y intercepts of 1 ?
(c) Find the equation of the line, n, through P that is perpendicular to the tangent line l.
(Line n is called the normal line to the graph of f at P.)
(d) Sketch a careful graph that displays: the graph of y = f (x), its vertex point, its
tangent and normal lines at point P, and the x and y intercepts of these lines.
Bonus: Find the coordinates of the second point, Q, (QP), at which the normal
line n intersects the graph of f.
2. A rock is thrown vertically upward with an initial velocity of 20 m/s
from the edge of a bridge that is 25 meters above a river bed. Based
on Newton's Laws of…
3. Use the graph for problem #35, p175 to answer the questions.
The average price (in cents) per gallon of unleaded gasoline in the United States for the years 2010 to 2019 is
shown in this chart. Find the average rate of change per year in the average price per gallon for each time
period. Source: U.S. Energy Information Administration.
a) 2010 to 2013
b) 2012 to 2018
c) 2014 to 2019
Chapter 11 Solutions
CALCULUS WITH APPLICATIONS
Ch. 11.1 - YOUR TURN 1 Repeat Example 1(a) for the function...Ch. 11.1 - Prob. 2YTCh. 11.1 - Prob. 3YTCh. 11.1 - Prob. 4YTCh. 11.1 - Prob. 1WECh. 11.1 - Prob. 2WECh. 11.1 - Prob. 3WECh. 11.1 - Decide whether the functions defined as follows...Ch. 11.1 - Decide whether the functions defined as follows...Ch. 11.1 - Decide whether the functions defined as follows...
Ch. 11.1 - Decide whether the functions defined as follows...Ch. 11.1 - Decide whether the functions defined as follows...Ch. 11.1 - Decide whether the functions defined as follows...Ch. 11.1 - Decide whether the functions defined as follows...Ch. 11.1 - Decide whether the functions defined as follows...Ch. 11.1 - Decide whether the functions defined as follows...Ch. 11.1 - Prob. 10ECh. 11.1 - Prob. 11ECh. 11.1 - Find a value of k that will make f a probability...Ch. 11.1 - Find a value of k that will make f a probability...Ch. 11.1 - Prob. 14ECh. 11.1 - Prob. 15ECh. 11.1 - Prob. 16ECh. 11.1 - Prob. 17ECh. 11.1 - Prob. 18ECh. 11.1 - Prob. 19ECh. 11.1 - Prob. 20ECh. 11.1 - Prob. 21ECh. 11.1 - Find the cumulative distribution function for the...Ch. 11.1 - Prob. 23ECh. 11.1 - Prob. 24ECh. 11.1 - 25. The total area under the graph of a...Ch. 11.1 - Prob. 26ECh. 11.1 - Prob. 27ECh. 11.1 - Prob. 28ECh. 11.1 - Show that each function defined as follows is a...Ch. 11.1 - Show that each function defined as follows is a...Ch. 11.1 - Prob. 31ECh. 11.1 - Show that each function defined as follows is a...Ch. 11.1 - Show that each function defined as follows is a...Ch. 11.1 - Show that each function defined as follows is a...Ch. 11.1 - 35. Life Span of a Computer Part The life (in...Ch. 11.1 - 36. Machine Life A machine has a useful life of 4...Ch. 11.1 - Prob. 37ECh. 11.1 - Prob. 38ECh. 11.1 - 39. Petal Length The length of a petal on a...Ch. 11.1 - 40. Clotting Time of Blood The clotting time of...Ch. 11.1 - 41. Flour Beetles Researchers who study the...Ch. 11.1 - 42. Flea Beetles The mobility of an insect is an...Ch. 11.1 - Prob. 43ECh. 11.1 - 44. Time to Learn a Task The time required for a...Ch. 11.1 - 45. Annual Rainfall The annual rainfall in a...Ch. 11.1 - Prob. 46ECh. 11.1 - 47. Earthquakes The time between major earthquakes...Ch. 11.1 - Prob. 48ECh. 11.1 - 49. Driving Fatalities We saw in a review exercise...Ch. 11.1 - Prob. 50ECh. 11.1 - Prob. 51ECh. 11.2 - YOUR TURN 1 Repeat Example l for the probability...Ch. 11.2 - Prob. 2YTCh. 11.2 - Prob. 3YTCh. 11.2 - Prob. 1WECh. 11.2 - Prob. 2WECh. 11.2 - In Exercises 1–8, a probability density function...Ch. 11.2 - In Exercises 1–8, a probability density function...Ch. 11.2 - Prob. 3ECh. 11.2 - In Exercises 1–8, a probability density function...Ch. 11.2 - Prob. 5ECh. 11.2 - Prob. 6ECh. 11.2 - In Exercises 1–8, a probability density function...Ch. 11.2 - In Exercises 1–8, a probability density function...Ch. 11.2 - 9. What information does the mean (expected value)...Ch. 11.2 - 10. Suppose two random variables have standard...Ch. 11.2 - In Exercises 11–14, the probability density...Ch. 11.2 - Prob. 12ECh. 11.2 - Prob. 13ECh. 11.2 - Prob. 14ECh. 11.2 - Prob. 15ECh. 11.2 - Prob. 16ECh. 11.2 - Prob. 17ECh. 11.2 - Prob. 18ECh. 11.2 - For Exercises 15–20, (a) find the median of the...Ch. 11.2 - For Exercises 15–20, (a) find the median of the...Ch. 11.2 - Find the expected value, the variance, and the...Ch. 11.2 - Prob. 22ECh. 11.2 - Prob. 23ECh. 11.2 - 24. Life of a Light Bulb The life (in hours) of a...Ch. 11.2 - 25. Machine Life The life (in years) of a certain...Ch. 11.2 - Prob. 26ECh. 11.2 - Prob. 27ECh. 11.2 - Prob. 28ECh. 11.2 - 29. Insurance Claims An insurance company’s...Ch. 11.2 - 30. Dental Insurance An insurance policy...Ch. 11.2 - 31. Blood Clotting Time The clotting time of blood...Ch. 11.2 - Prob. 32ECh. 11.2 - 33. Petal Length The length (in centimeters) of a...Ch. 11.2 - Prob. 34ECh. 11.2 - 35. Flour Beetles As we saw in Exercise 41 of the...Ch. 11.2 - Prob. 36ECh. 11.2 - 37. Social Network In Exercise 43 of the previous...Ch. 11.2 - 38. Earthquakes The time between major earthquakes...Ch. 11.2 - 39. Annual Rainfall The annual rainfall in a...Ch. 11.2 - Prob. 40ECh. 11.2 - Prob. 41ECh. 11.2 - Prob. 42ECh. 11.2 - 43. Time of Traffic Fatality In Exercise 51 of the...Ch. 11.3 - YOUR TURN 1 The next vacation for the couple in...Ch. 11.3 - Prob. 2YTCh. 11.3 - Prob. 3YTCh. 11.3 - Evaluate each of the following integrals. (Sec....Ch. 11.3 - Prob. 2WECh. 11.3 - Prob. 1ECh. 11.3 - Find (a) the mean of the distribution, (b) the...Ch. 11.3 - Find (a) the mean of the distribution, (b) the...Ch. 11.3 - Find (a) the mean of the distribution, (b) the...Ch. 11.3 - Prob. 5ECh. 11.3 - Prob. 6ECh. 11.3 - Find the proportion of observations of a standard...Ch. 11.3 - Find the proportion of observations of a standard...Ch. 11.3 - Prob. 9ECh. 11.3 - Prob. 10ECh. 11.3 - Prob. 11ECh. 11.3 - Prob. 12ECh. 11.3 - Find a z-score satisfying the conditions given in...Ch. 11.3 - Prob. 14ECh. 11.3 - Prob. 15ECh. 11.3 - Prob. 16ECh. 11.3 - Prob. 17ECh. 11.3 - In the second section of this chapter, we defined...Ch. 11.3 - Prob. 19ECh. 11.3 - Prob. 20ECh. 11.3 - Prob. 21ECh. 11.3 - Prob. 22ECh. 11.3 - Prob. 23ECh. 11.3 - Prob. 24ECh. 11.3 - Prob. 25ECh. 11.3 - Prob. 26ECh. 11.3 - Prob. 27ECh. 11.3 - 28. Determine the cumulative distribution function...Ch. 11.3 - 29. Insurance Sales The amount of insurance (in...Ch. 11.3 - Prob. 30ECh. 11.3 - 31. Sales Expense A salesperson’s monthly expenses...Ch. 11.3 - 32. Machine Accuracy A machine that fills quart...Ch. 11.3 - 33. Machine Accuracy A machine produces screws...Ch. 11.3 - Prob. 34ECh. 11.3 - 35. Insured Loss An insurance policy is written to...Ch. 11.3 - Prob. 36ECh. 11.3 - 37. Printer Failure The lifetime of a printer...Ch. 11.3 - Prob. 38ECh. 11.3 - Prob. 39ECh. 11.3 - Prob. 40ECh. 11.3 - 41. Digestion Time The digestion time (in hours)...Ch. 11.3 - Prob. 42ECh. 11.3 - 43. Finding Prey H. R. Pulliam found that the time...Ch. 11.3 - Prob. 44ECh. 11.3 - Prob. 45ECh. 11.3 - 46. Mercury Poisoning Historians and biographers...Ch. 11.3 - Prob. 47ECh. 11.3 - Prob. 48ECh. 11.3 - Prob. 49ECh. 11.3 - Prob. 50ECh. 11.3 - Prob. 51ECh. 11.3 - Prob. 52ECh. 11.3 - Prob. 53ECh. 11.3 - Prob. 54ECh. 11 - Prob. 1RECh. 11 - Prob. 2RECh. 11 - Prob. 3RECh. 11 - Prob. 4RECh. 11 - Prob. 5RECh. 11 - Prob. 6RECh. 11 - Prob. 7RECh. 11 - Prob. 8RECh. 11 - Prob. 9RECh. 11 - Prob. 10RECh. 11 - Prob. 11RECh. 11 - Prob. 12RECh. 11 - Prob. 13RECh. 11 - Prob. 14RECh. 11 - Prob. 15RECh. 11 - Prob. 16RECh. 11 - Prob. 17RECh. 11 - Prob. 18RECh. 11 - Prob. 19RECh. 11 - Prob. 20RECh. 11 - Prob. 21RECh. 11 - Prob. 22RECh. 11 - Prob. 23RECh. 11 - Prob. 24RECh. 11 - Prob. 25RECh. 11 - Prob. 26RECh. 11 - Prob. 27RECh. 11 - Prob. 28RECh. 11 - Prob. 29RECh. 11 - Prob. 30RECh. 11 - Prob. 31RECh. 11 - Prob. 32RECh. 11 - Prob. 33RECh. 11 - Prob. 34RECh. 11 - Prob. 35RECh. 11 - Prob. 36RECh. 11 - Prob. 37RECh. 11 - Prob. 38RECh. 11 - Prob. 39RECh. 11 - Prob. 40RECh. 11 - Prob. 41RECh. 11 - Prob. 42RECh. 11 - Prob. 43RECh. 11 - Prob. 44RECh. 11 - 45. When the degrees of freedom in the chi-square...Ch. 11 - Prob. 46RECh. 11 - Prob. 47RECh. 11 - Prob. 48RECh. 11 - Prob. 49RECh. 11 - Prob. 50RECh. 11 - Prob. 51RECh. 11 - Prob. 52RECh. 11 - Prob. 53RECh. 11 - Prob. 54RECh. 11 - Prob. 55RECh. 11 - Prob. 56RECh. 11 - Prob. 57RECh. 11 - Prob. 58RECh. 11 - Prob. 59RECh. 11 - 60. Assaults The number of deaths in the United...Ch. 11 - Prob. 61RECh. 11 - Prob. 62RE
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