Precalculus (10th Edition)
10th Edition
ISBN: 9780321979070
Author: Michael Sullivan
Publisher: PEARSON
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Chapter 14.3, Problem 9AYU
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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…
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 14 Solutions
Precalculus (10th Edition)
Ch. 14.1 - Graph f( x )={ 3x2ifx2 3ifx=2 (pp.100-102)Ch. 14.1 - Prob. 2AYUCh. 14.1 - Prob. 3AYUCh. 14.1 - Prob. 4AYUCh. 14.1 - True or False lim xc f( x )=N may be described by...Ch. 14.1 - Prob. 6AYUCh. 14.1 - lim x2 ( 4 x 3 )Ch. 14.1 - lim x3 ( 2 x 2 +1 )Ch. 14.1 - Prob. 9AYUCh. 14.1 - Prob. 10AYU
Ch. 14.1 - Prob. 11AYUCh. 14.1 - Prob. 12AYUCh. 14.1 - Prob. 13AYUCh. 14.1 - Prob. 14AYUCh. 14.1 - Prob. 15AYUCh. 14.1 - Prob. 16AYUCh. 14.1 - In Problems 17-22, use the graph shown to...Ch. 14.1 - In Problems 17-22, use the graph shown to...Ch. 14.1 - In Problems 17-22, use the graph shown to...Ch. 14.1 - Prob. 20AYUCh. 14.1 - In Problems 17-22, use the graph shown to...Ch. 14.1 - Prob. 22AYUCh. 14.1 - Prob. 23AYUCh. 14.1 - Prob. 24AYUCh. 14.1 - Prob. 25AYUCh. 14.1 - Prob. 26AYUCh. 14.1 - In Problems 23-42, graph each function. Use the...Ch. 14.1 - Prob. 28AYUCh. 14.1 - Prob. 29AYUCh. 14.1 - Prob. 30AYUCh. 14.1 - In Problems 23-42, graph each function. Use the...Ch. 14.1 - Prob. 32AYUCh. 14.1 - Prob. 33AYUCh. 14.1 - Prob. 34AYUCh. 14.1 - In Problems 23-42, graph each function. Use the...Ch. 14.1 - In Problems 23-42, graph each function. Use the...Ch. 14.1 - In Problems 23-42, graph each function. Use the...Ch. 14.1 - Prob. 38AYUCh. 14.1 - Prob. 39AYUCh. 14.1 - Prob. 40AYUCh. 14.1 - Prob. 41AYUCh. 14.1 - Prob. 42AYUCh. 14.1 - In Problems 43-48, use a graphing utility to find...Ch. 14.1 - Prob. 44AYUCh. 14.1 - Prob. 45AYUCh. 14.1 - Prob. 46AYUCh. 14.1 - Prob. 47AYUCh. 14.1 - In Problems 43-48, use a graphing utility to find...Ch. 14.1 - Prob. 49AYUCh. 14.1 - Prob. 50AYUCh. 14.1 - Prob. 51AYUCh. 14.1 - Prob. 52AYUCh. 14.2 - Prob. 1AYUCh. 14.2 - Prob. 2AYUCh. 14.2 - Prob. 3AYUCh. 14.2 - Prob. 4AYUCh. 14.2 - Prob. 5AYUCh. 14.2 - Prob. 6AYUCh. 14.2 - In Problems 7- 42, find each limit algebraically....Ch. 14.2 - Prob. 8AYUCh. 14.2 - In Problems 7-42, find each limit algebraically....Ch. 14.2 - Prob. 10AYUCh. 14.2 - Prob. 11AYUCh. 14.2 - In Problems 7-42, find each limit algebraically....Ch. 14.2 - Prob. 13AYUCh. 14.2 - Prob. 14AYUCh. 14.2 - In Problems 7-42, find each limit algebraically....Ch. 14.2 - In Problems 7-42, find each limit algebraically....Ch. 14.2 - Prob. 17AYUCh. 14.2 - Prob. 18AYUCh. 14.2 - In Problems 7-42, find each limit algebraically....Ch. 14.2 - In Problems 7-42, find each limit algebraically....Ch. 14.2 - Prob. 21AYUCh. 14.2 - Prob. 22AYUCh. 14.2 - In Problems 7-42, find each limit algebraically....Ch. 14.2 - Prob. 24AYUCh. 14.2 - In Problems 7-42, find each limit algebraically....Ch. 14.2 - Prob. 26AYUCh. 14.2 - In Problems 7-42, find each limit algebraically....Ch. 14.2 - Prob. 28AYUCh. 14.2 - In Problems 7-42, find each limit algebraically....Ch. 14.2 - Prob. 30AYUCh. 14.2 - In Problems 7-42, find each limit algebraically....Ch. 14.2 - Prob. 32AYUCh. 14.2 - In Problems 7-42, find each limit algebraically....Ch. 14.2 - Prob. 34AYUCh. 14.2 - Prob. 35AYUCh. 14.2 - In Problems 7-42, find each limit algebraically....Ch. 14.2 - Prob. 37AYUCh. 14.2 - Prob. 38AYUCh. 14.2 - Prob. 39AYUCh. 14.2 - Prob. 40AYUCh. 14.2 - Prob. 41AYUCh. 14.2 - Prob. 42AYUCh. 14.2 - In Problems 43-52, find the limit as x approaches...Ch. 14.2 - Prob. 44AYUCh. 14.2 - Prob. 45AYUCh. 14.2 - Prob. 46AYUCh. 14.2 - Prob. 47AYUCh. 14.2 - In Problems 43-52, find the limit as x approaches...Ch. 14.2 - Prob. 49AYUCh. 14.2 - Prob. 50AYUCh. 14.2 - Prob. 51AYUCh. 14.2 - Prob. 52AYUCh. 14.2 - In problems 53-56, use the properties of limits...Ch. 14.2 - Prob. 54AYUCh. 14.2 - Prob. 55AYUCh. 14.2 - In problems 53-56, use the properties of limits...Ch. 14.2 - Prob. 57AYUCh. 14.2 - Prob. 58AYUCh. 14.2 - Prob. 59AYUCh. 14.2 - Prob. 60AYUCh. 14.3 - For the function f( x )={ x 2 ifx0 x+1if0x2...Ch. 14.3 - Prob. 2AYUCh. 14.3 - Prob. 3AYUCh. 14.3 - Prob. 4AYUCh. 14.3 - Prob. 5AYUCh. 14.3 - Prob. 6AYUCh. 14.3 - Prob. 7AYUCh. 14.3 - Prob. 8AYUCh. 14.3 - Prob. 9AYUCh. 14.3 - Prob. 10AYUCh. 14.3 - Prob. 11AYUCh. 14.3 - In Problems 7-42, find each limit algebraically....Ch. 14.3 - In Problems 7-42, find each limit algebraically....Ch. 14.3 - Prob. 14AYUCh. 14.3 - Prob. 15AYUCh. 14.3 - Prob. 16AYUCh. 14.3 - Prob. 17AYUCh. 14.3 - Prob. 18AYUCh. 14.3 - In Problems 7-42, find each limit algebraically....Ch. 14.3 - Prob. 20AYUCh. 14.3 - Find lim x 4 f( x ) .Ch. 14.3 - Prob. 22AYUCh. 14.3 - Find lim x 2 f( x ) .Ch. 14.3 - Prob. 24AYUCh. 14.3 - Does lim x4 f( x ) exist? If it does, what is it?Ch. 14.3 - Prob. 26AYUCh. 14.3 - Is f continuous at 4 ?Ch. 14.3 - Prob. 28AYUCh. 14.3 - Is f continuous at 0?Ch. 14.3 - Prob. 30AYUCh. 14.3 - Is f continuous at 4?Ch. 14.3 - Prob. 32AYUCh. 14.3 - Prob. 33AYUCh. 14.3 - Prob. 34AYUCh. 14.3 - Prob. 35AYUCh. 14.3 - Prob. 36AYUCh. 14.3 - Prob. 37AYUCh. 14.3 - Prob. 38AYUCh. 14.3 - lim x 2 + x 2 4 x2Ch. 14.3 - lim x 1 x 3 x x1Ch. 14.3 - lim x 1 x 2 1 x 3 +1Ch. 14.3 - Prob. 42AYUCh. 14.3 - Prob. 43AYUCh. 14.3 - Prob. 44AYUCh. 14.3 - Prob. 45AYUCh. 14.3 - Prob. 46AYUCh. 14.3 - Prob. 47AYUCh. 14.3 - Prob. 48AYUCh. 14.3 - f( x )= x+3 x3 c=3Ch. 14.3 - Prob. 50AYUCh. 14.3 - Prob. 51AYUCh. 14.3 - Prob. 52AYUCh. 14.3 - Prob. 53AYUCh. 14.3 - Prob. 54AYUCh. 14.3 - Prob. 55AYUCh. 14.3 - Prob. 56AYUCh. 14.3 - f( x )={ x 3 1 x 2 1 ifx1 2ifx=1 3 x+1 ifx1 c=1Ch. 14.3 - Prob. 58AYUCh. 14.3 - Prob. 61AYUCh. 14.3 - Prob. 62AYUCh. 14.3 - Prob. 63AYUCh. 14.3 - Prob. 64AYUCh. 14.3 - Prob. 65AYUCh. 14.3 - Prob. 66AYUCh. 14.3 - Prob. 67AYUCh. 14.3 - Prob. 68AYUCh. 14.3 - f( x )= 2x+5 x 2 4Ch. 14.3 - Prob. 70AYUCh. 14.3 - Prob. 71AYUCh. 14.3 - Prob. 72AYUCh. 14.3 - Prob. 73AYUCh. 14.3 - Prob. 74AYUCh. 14.3 - Prob. 75AYUCh. 14.3 - Prob. 76AYUCh. 14.3 - Prob. 77AYUCh. 14.3 - Prob. 78AYUCh. 14.3 - Prob. 79AYUCh. 14.3 - Prob. 80AYUCh. 14.3 - Prob. 81AYUCh. 14.3 - Prob. 82AYUCh. 14.3 - Prob. 83AYUCh. 14.3 - Prob. 84AYUCh. 14.3 - Prob. 85AYUCh. 14.3 - Prob. 86AYUCh. 14.3 - Prob. 87AYUCh. 14.3 - Prob. 88AYUCh. 14.3 - Prob. 89AYUCh. 14.3 - Prob. 90AYUCh. 14.3 - Prob. 91AYUCh. 14.3 - Prob. 92AYUCh. 14.3 - Prob. 93AYUCh. 14.3 - Prob. 94AYUCh. 14.4 - Prob. 1AYUCh. 14.4 - Prob. 2AYUCh. 14.4 - Prob. 3AYUCh. 14.4 - lim xc f( x )f( c ) xc exists, it is called the...Ch. 14.4 - Prob. 5AYUCh. 14.4 - Prob. 6AYUCh. 14.4 - Prob. 7AYUCh. 14.4 - Prob. 8AYUCh. 14.4 - Prob. 9AYUCh. 14.4 - f( x )=2x+1 at ( 1,3 )Ch. 14.4 - Prob. 11AYUCh. 14.4 - Prob. 12AYUCh. 14.4 - Prob. 13AYUCh. 14.4 - Prob. 14AYUCh. 14.4 - Prob. 15AYUCh. 14.4 - Prob. 16AYUCh. 14.4 - Prob. 17AYUCh. 14.4 - Prob. 18AYUCh. 14.4 - Prob. 19AYUCh. 14.4 - Prob. 20AYUCh. 14.4 - Prob. 21AYUCh. 14.4 - Prob. 22AYUCh. 14.4 - Prob. 23AYUCh. 14.4 - Prob. 24AYUCh. 14.4 - Prob. 25AYUCh. 14.4 - Prob. 26AYUCh. 14.4 - Prob. 27AYUCh. 14.4 - Prob. 28AYUCh. 14.4 - Prob. 29AYUCh. 14.4 - Prob. 30AYUCh. 14.4 - Prob. 31AYUCh. 14.4 - Prob. 32AYUCh. 14.4 - Prob. 33AYUCh. 14.4 - Prob. 34AYUCh. 14.4 - Prob. 35AYUCh. 14.4 - Prob. 36AYUCh. 14.4 - Prob. 37AYUCh. 14.4 - Prob. 38AYUCh. 14.4 - Prob. 39AYUCh. 14.4 - Prob. 40AYUCh. 14.4 - Prob. 41AYUCh. 14.4 - Prob. 42AYUCh. 14.4 - Prob. 43AYUCh. 14.4 - Prob. 44AYUCh. 14.4 - Prob. 45AYUCh. 14.4 - Prob. 46AYUCh. 14.4 - Prob. 47AYUCh. 14.4 - Prob. 48AYUCh. 14.4 - Instantaneous Velocity on the Moon Neil Armstrong...Ch. 14.4 - Prob. 50AYUCh. 14.4 - Prob. 51AYUCh. 14.4 - Prob. 52AYUCh. 14.4 - Prob. 53AYUCh. 14.4 - Prob. 54AYUCh. 14.5 - In Problems 29-32, find the first five terms in...Ch. 14.5 - Prob. 2AYUCh. 14.5 - Prob. 3AYUCh. 14.5 - Prob. 4AYUCh. 14.5 - In Problems 5 and 6, refer to the illustration....Ch. 14.5 - Prob. 6AYUCh. 14.5 - Prob. 7AYUCh. 14.5 - Prob. 8AYUCh. 14.5 - Prob. 9AYUCh. 14.5 - Prob. 10AYUCh. 14.5 - The function is defined on the interval
Graph
In...Ch. 14.5 - Prob. 12AYUCh. 14.5 - Prob. 13AYUCh. 14.5 - Prob. 14AYUCh. 14.5 - Prob. 15AYUCh. 14.5 - Prob. 16AYUCh. 14.5 - Prob. 17AYUCh. 14.5 - Prob. 18AYUCh. 14.5 - Prob. 19AYUCh. 14.5 - Prob. 20AYUCh. 14.5 - Prob. 21AYUCh. 14.5 - Prob. 22AYUCh. 14.5 - Prob. 23AYUCh. 14.5 - Prob. 24AYUCh. 14.5 - In Problems 23-30, an integral is given. (a) What...Ch. 14.5 - Prob. 26AYUCh. 14.5 - Prob. 27AYUCh. 14.5 - Prob. 28AYUCh. 14.5 - Prob. 29AYUCh. 14.5 - Prob. 30AYUCh. 14.5 - Prob. 31AYUCh. 14.5 - Prob. 32AYUCh. 14.5 - Prob. 33AYUCh. 14.5 - Prob. 34AYUCh. 14.5 - Prob. 35AYUCh. 14.5 - Prob. 36AYUCh. 14 - In Problems, find the limit.
Ch. 14 - In Problems, find the limit.
Ch. 14 - Prob. 3RECh. 14 - Prob. 4RECh. 14 - Prob. 5RECh. 14 - Prob. 6RECh. 14 - Prob. 7RECh. 14 - Prob. 8RECh. 14 - Prob. 9RECh. 14 - Prob. 10RECh. 14 - Prob. 11RECh. 14 - Prob. 12RECh. 14 - Prob. 13RECh. 14 - In Problems 1215, determine whether fis continuous...Ch. 14 - Prob. 15RECh. 14 - Prob. 16RECh. 14 - Prob. 17RECh. 14 - Prob. 18RECh. 14 - Prob. 19RECh. 14 - Prob. 20RECh. 14 - Prob. 21RECh. 14 - In Problems, use the accompanying graph of ....Ch. 14 - In Problems 1627, use the accompanying graph of...Ch. 14 - In Problems, use the accompanying graph of .
Find...Ch. 14 - In Problems, use the accompanying graph of .
Does...Ch. 14 - In Problems 1627, use the accompanying graph of...Ch. 14 - In Problems, use the accompanying graph of .
Is...Ch. 14 - Discuss whether is continuous at and . Use limits...Ch. 14 - Determine where the rational function is...Ch. 14 - In Problems, find the slope of the tangent line to...Ch. 14 - In Problems 3032, find the slope of the tangent...Ch. 14 - In Problems, find the slope of the tangent line to...Ch. 14 - In Problems 3335, find the derivative of each...Ch. 14 - In Problems 3335, find the derivative of each...Ch. 14 - In Problems 3335, find the derivative of each...Ch. 14 - In Problems 36 and 37, approximate the derivative...Ch. 14 - In Problems and, approximate the derivative of...Ch. 14 - Instantaneous Velocity of a Ball In physics it is...Ch. 14 - Instantaneous Rate of Change The following data...Ch. 14 - Prob. 40RECh. 14 - Prob. 41RECh. 14 - Prob. 42RECh. 14 - Prob. 43RECh. 14 - Prob. 44RECh. 14 - Prob. 1CTCh. 14 - Prob. 2CTCh. 14 - Prob. 3CTCh. 14 - Prob. 4CTCh. 14 - Prob. 5CTCh. 14 - Prob. 6CTCh. 14 - Prob. 7CTCh. 14 - Prob. 8CTCh. 14 - Prob. 9CTCh. 14 - Prob. 10CTCh. 14 - Prob. 11CTCh. 14 - Prob. 12CTCh. 14 - Prob. 13CTCh. 14 - Prob. 14CTCh. 14 - Prob. 15CTCh. 14 - Prob. 16CTCh. 14 - An object is moving along a straight line...
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