CALCULUS+ITS APPLICATIONS-MYMATHLAB
15th Edition
ISBN: 9780137590438
Author: Goldstein
Publisher: PEARSON
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Chapter 12.4, Problem 36E
To determine
To graph: The function
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W₂
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The revenue (in thousands of dollars) from producing x units of an item is R(x)=8x-0.015 x².
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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…
Chapter 12 Solutions
CALCULUS+ITS APPLICATIONS-MYMATHLAB
Ch. 12.1 - Compute the expected value and the variance of the...Ch. 12.1 - Prob. 2CYUCh. 12.1 - Prob. 1ECh. 12.1 - Prob. 2ECh. 12.1 - Prob. 3ECh. 12.1 - Prob. 4ECh. 12.1 - Prob. 5ECh. 12.1 - Probability Table, Expected Value The number of...Ch. 12.1 - Prob. 7ECh. 12.1 - Prob. 8E
Ch. 12.1 - Decision Making Based on Expected Value A citrus...Ch. 12.1 - Prob. 10ECh. 12.2 - Prob. 1CYUCh. 12.2 - Prob. 2CYUCh. 12.2 - Prob. 1ECh. 12.2 - Prob. 2ECh. 12.2 - Prob. 3ECh. 12.2 - Prob. 4ECh. 12.2 - Prob. 5ECh. 12.2 - Prob. 6ECh. 12.2 - Prob. 7ECh. 12.2 - Prob. 8ECh. 12.2 - Prob. 9ECh. 12.2 - Prob. 10ECh. 12.2 - Prob. 11ECh. 12.2 - Prob. 12ECh. 12.2 - Prob. 13ECh. 12.2 - Prob. 14ECh. 12.2 - Prob. 15ECh. 12.2 - Prob. 16ECh. 12.2 - Prob. 17ECh. 12.2 - Prob. 18ECh. 12.2 - Prob. 19ECh. 12.2 - Prob. 20ECh. 12.2 - Prob. 21ECh. 12.2 - Prob. 22ECh. 12.2 - Prob. 23ECh. 12.2 - Prob. 24ECh. 12.2 - Prob. 25ECh. 12.2 - Prob. 26ECh. 12.2 - An experiment consists of selecting a point at...Ch. 12.2 - Prob. 28ECh. 12.2 - Prob. 29ECh. 12.2 - Prob. 30ECh. 12.2 - Prob. 31ECh. 12.2 - Prob. 32ECh. 12.2 - Prob. 33ECh. 12.2 - Prob. 34ECh. 12.2 - Prob. 35ECh. 12.2 - A random variable X has a cumulative distribution...Ch. 12.2 - Prob. 37ECh. 12.2 - Prob. 38ECh. 12.3 - Prob. 1CYUCh. 12.3 - Prob. 2CYUCh. 12.3 - Prob. 1ECh. 12.3 - Prob. 2ECh. 12.3 - Prob. 3ECh. 12.3 - Prob. 4ECh. 12.3 - Prob. 5ECh. 12.3 - Prob. 6ECh. 12.3 - Prob. 7ECh. 12.3 - Prob. 8ECh. 12.3 - Prob. 9ECh. 12.3 - Prob. 10ECh. 12.3 - Prob. 11ECh. 12.3 - Prob. 12ECh. 12.3 - Expected Reading Time The amount oftime (in...Ch. 12.3 - Prob. 14ECh. 12.3 - Prob. 15ECh. 12.3 - Prob. 16ECh. 12.3 - Prob. 17ECh. 12.3 - Prob. 18ECh. 12.3 - If X is a random variable with density function...Ch. 12.3 - Prob. 20ECh. 12.3 - Prob. 21ECh. 12.3 - Prob. 22ECh. 12.3 - Prob. 23ECh. 12.3 - Prob. 24ECh. 12.3 - Prob. 25ECh. 12.3 - Prob. 26ECh. 12.4 - The emergency flasher on an automobile is...Ch. 12.4 - Prob. 2CYUCh. 12.4 - Prob. 1ECh. 12.4 - Prob. 2ECh. 12.4 - Prob. 3ECh. 12.4 - Prob. 4ECh. 12.4 - Prob. 5ECh. 12.4 - In a large factory there is an average of two...Ch. 12.4 - Prob. 7ECh. 12.4 - Prob. 8ECh. 12.4 - During a certain part of the day, the time between...Ch. 12.4 - During a certain part of the day, the time between...Ch. 12.4 - Prob. 11ECh. 12.4 - Prob. 12ECh. 12.4 - Reliability of Electronic Components Suppose that...Ch. 12.4 - Prob. 14ECh. 12.4 - Prob. 15ECh. 12.4 - Find the expected values and the standard...Ch. 12.4 - Prob. 17ECh. 12.4 - Find the expected values and the standard...Ch. 12.4 - Prob. 19ECh. 12.4 - Prob. 20ECh. 12.4 - Prob. 21ECh. 12.4 - Prob. 22ECh. 12.4 - Prob. 23ECh. 12.4 - Prob. 24ECh. 12.4 - Prob. 25ECh. 12.4 - Normal Distribution and Life of a Tire Suppose...Ch. 12.4 - Amount of Milk in a Container If the amount of...Ch. 12.4 - Breaking weight Theamount of weight required to...Ch. 12.4 - Time of a commute A student with an eight oclock...Ch. 12.4 - Prob. 30ECh. 12.4 - Diameter of a Bolt A certain type of bolt must fit...Ch. 12.4 - Prob. 32ECh. 12.4 - Prob. 33ECh. 12.4 - Prob. 34ECh. 12.4 - Prob. 35ECh. 12.4 - Prob. 36ECh. 12.4 - Prob. 37ECh. 12.5 - A public health officer is tracking down the...Ch. 12.5 - Suppose that a random variable X has a Poisson...Ch. 12.5 - Prob. 2ECh. 12.5 - Prob. 3ECh. 12.5 - Prob. 4ECh. 12.5 - Number of Insurance Claims The monthly number of...Ch. 12.5 - Waiting Time in an Emergency Room On a typical...Ch. 12.5 - Prob. 7ECh. 12.5 - Number of Cars at a Tollgate During a certain part...Ch. 12.5 - Poisson Distribution in a Mixing Problem A bakery...Ch. 12.5 - Prob. 10ECh. 12.5 - Prob. 11ECh. 12.5 - Quality Control The quality-control department at...Ch. 12.5 - Two Competing Companies In a certain town, there...Ch. 12.5 - Prob. 14ECh. 12.5 - Prob. 15ECh. 12.5 - Prob. 16ECh. 12.5 - Prob. 17ECh. 12.5 - Prob. 18ECh. 12.5 - Prob. 19ECh. 12.5 - Prob. 20ECh. 12.5 - Prob. 21ECh. 12.5 - Prob. 22ECh. 12.5 - Prob. 23ECh. 12.5 - Prob. 24ECh. 12.5 - Prob. 25ECh. 12.5 - The number of accidents occurring each month at a...Ch. 12 - What is probability table?Ch. 12 - Prob. 2FCCECh. 12 - Prob. 3FCCECh. 12 - Prob. 4FCCECh. 12 - Prob. 5FCCECh. 12 - Prob. 6FCCECh. 12 - Prob. 7FCCECh. 12 - Prob. 8FCCECh. 12 - Prob. 9FCCECh. 12 - Give two ways to compute the variance of a...Ch. 12 - Prob. 11FCCECh. 12 - Prob. 12FCCECh. 12 - Prob. 13FCCECh. 12 - Prob. 14FCCECh. 12 - How is an integral involving a normal density...Ch. 12 - Prob. 16FCCECh. 12 - Prob. 17FCCECh. 12 - Let X be a continuous random variable on 0x2, with...Ch. 12 - Prob. 2RECh. 12 - Prob. 3RECh. 12 - Prob. 4RECh. 12 - Prob. 5RECh. 12 - Prob. 6RECh. 12 - Prob. 7RECh. 12 - Prob. 8RECh. 12 - Probability of Gasoline Sales A certain gas...Ch. 12 - Prob. 10RECh. 12 - Prob. 11RECh. 12 - Prob. 12RECh. 12 - Prob. 13RECh. 12 - Prob. 14RECh. 12 - Prob. 15RECh. 12 - Prob. 16RECh. 12 - Prob. 17RECh. 12 - Deciding on a Service Contract The condenser motor...Ch. 12 - Prob. 19RECh. 12 - Prob. 20RECh. 12 - Prob. 21RECh. 12 - Prob. 22RECh. 12 - Prob. 23RECh. 12 - Prob. 24RECh. 12 - Prob. 25RECh. 12 - Prob. 26RECh. 12 - Area under the Normal Curve It is useful in some...Ch. 12 - Prob. 28RECh. 12 - Prob. 29RECh. 12 - Prob. 30RECh. 12 - Prob. 31RECh. 12 - Prob. 32RECh. 12 - Prob. 33RECh. 12 - Rolling Dice A pair of dice is rolled until a 7 or...Ch. 12 - Rolling Dice A pair of dice is rolled until a 7 or...Ch. 12 - Rolling Dice A pair of dice is rolled until a 7 or...
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