Precalculus Enhanced with Graphing Utilities (7th Edition)
7th Edition
ISBN: 9780134119281
Author: Michael Sullivan, Michael Sullivan III
Publisher: PEARSON
expand_more
expand_more
format_list_bulleted
Concept explainers
Videos
Textbook Question
Chapter 14.1, Problem 33SB
In Problems 23-42, graph each function. Use the graph to find the indicated limit, if it exists.
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
Given lim x-4 f (x) = 1,limx-49 (x) = 10, and lim→-4 h (x) = -7 use the limit properties
to find lim→-4
1
[2h (x) — h(x) + 7 f(x)] :
-
h(x)+7f(x)
3
O DNE
17. Suppose we know that the graph below is the graph of a solution to dy/dt = f(t).
(a) How much of the slope field can
you sketch from this information?
[Hint: Note that the differential
equation depends only on t.]
(b) What can you say about the solu-
tion with y(0) = 2? (For example,
can you sketch the graph of this so-
lution?)
y(0) = 1
y
AN
(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
Chapter 14 Solutions
Precalculus Enhanced with Graphing Utilities (7th Edition)
Ch. 14.1 - Graph f( x )={ 3x2ifx2 3ifx=2 (pp.100-102)Ch. 14.1 - If f( x )={ xifx0 1ifx0 what is f( 0 ) ?...Ch. 14.1 - The limit of a function f( x ) as x approaches c...Ch. 14.1 - If a function f has no limit as x approaches c ,...Ch. 14.1 - True or False lim xc f( x )=N may be described by...Ch. 14.1 - True or False lim xc f( x ) exists and equals some...Ch. 14.1 - lim x2 ( 4 x 3 )Ch. 14.1 - lim x3 ( 2 x 2 +1 )Ch. 14.1 - lim x0 x+1 x 2 +1Ch. 14.1 - lim x0 2x x 2 +4
Ch. 14.1 - lim x4 x 2 4x x4Ch. 14.1 - lim x3 x 2 9 x 2 3xCh. 14.1 - lim x0 ( e x +1 )Ch. 14.1 - Prob. 14SBCh. 14.1 - lim x0 cosx1 x , x in radiansCh. 14.1 - lim x0 tanx x , x in radiansCh. 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 - 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 - 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 - 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 - 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 - 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 - 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 - 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 - 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 43-48, use a graphing utility to find...Ch. 14.1 - In Problems 43-48, use a graphing utility to find...Ch. 14.1 - In Problems 43-48, use a graphing utility to find...Ch. 14.1 - In Problems 43-48, use a graphing utility to find...Ch. 14.1 - In Problems 43-48, use a graphing utility to find...Ch. 14.1 - In Problems 43-48, use a graphing utility to find...Ch. 14.1 - Problems 49-52 are based on material learned...Ch. 14.1 - Problems 49-52 are based on material learned...Ch. 14.1 - Problems 49-52 are based on material learned...Ch. 14.1 - Problems 49-52 are based on material learned...Ch. 14.2 - The limit of the product of two functions equals...Ch. 14.2 - lim xc b= _____Ch. 14.2 - lim xc x= a. x b. c c. cx d. x cCh. 14.2 - True or False The limit of a polynomial function...Ch. 14.2 - True or False The limit of a rational function at...Ch. 14.2 - True or false The limit of a quotient equals the...Ch. 14.2 - In Problems 7- 42, find each limit algebraically....Ch. 14.2 - In Problems 7- 42, find each limit algebraically....Ch. 14.2 - In Problems 7-42, find each limit algebraically....Ch. 14.2 - In Problems 7-42, find each limit algebraically....Ch. 14.2 - In Problems 7-42, find each limit algebraically....Ch. 14.2 - In Problems 7-42, find each limit algebraically....Ch. 14.2 - In Problems 7-42, find each limit algebraically....Ch. 14.2 - In Problems 7-42, find each limit algebraically....Ch. 14.2 - In Problems 7-42, find each limit algebraically....Ch. 14.2 - In Problems 7-42, find each limit algebraically....Ch. 14.2 - In Problems 7-42, find each limit algebraically....Ch. 14.2 - In Problems 7-42, find each limit algebraically....Ch. 14.2 - In Problems 7-42, find each limit algebraically....Ch. 14.2 - In Problems 7-42, find each limit algebraically....Ch. 14.2 - In Problems 7-42, find each limit algebraically....Ch. 14.2 - In Problems 7-42, find each limit algebraically....Ch. 14.2 - In Problems 7-42, find each limit algebraically....Ch. 14.2 - In Problems 7-42, find each limit algebraically....Ch. 14.2 - In Problems 7-42, find each limit algebraically....Ch. 14.2 - In Problems 7-42, find each limit algebraically....Ch. 14.2 - In Problems 7-42, find each limit algebraically....Ch. 14.2 - In Problems 7-42, find each limit algebraically....Ch. 14.2 - In Problems 7-42, find each limit algebraically....Ch. 14.2 - In Problems 7-42, find each limit algebraically....Ch. 14.2 - In Problems 7-42, find each limit algebraically....Ch. 14.2 - In Problems 7-42, find each limit algebraically....Ch. 14.2 - In Problems 7-42, find each limit algebraically....Ch. 14.2 - In Problems 7-42, find each limit algebraically....Ch. 14.2 - In Problems 7-42, find each limit algebraically....Ch. 14.2 - In Problems 7-42, find each limit algebraically....Ch. 14.2 - In Problems 7-42, find each limit algebraically....Ch. 14.2 - In Problems 7-42, find each limit algebraically....Ch. 14.2 - In Problems 7-42, find each limit algebraically....Ch. 14.2 - In Problems 7-42, find each limit algebraically....Ch. 14.2 - In Problems 7-42, find each limit algebraically....Ch. 14.2 - In Problems 7-42, find each limit algebraically....Ch. 14.2 - In Problems 43-52, find the limit as x approaches...Ch. 14.2 - In Problems 43-52, find the limit as x approaches...Ch. 14.2 - In Problems 43-52, find the limit as x approaches...Ch. 14.2 - In Problems 43-52, find the limit as x approaches...Ch. 14.2 - In Problems 43-52, find the limit as x approaches...Ch. 14.2 - In Problems 43-52, find the limit as x approaches...Ch. 14.2 - In Problems 43-52, find the limit as x approaches...Ch. 14.2 - In Problems 43-52, find the limit as x approaches...Ch. 14.2 - In Problems 43-52, find the limit as x approaches...Ch. 14.2 - In Problems 43-52, find the limit as x approaches...Ch. 14.2 - In problems 53-56, use the properties of limits...Ch. 14.2 - In problems 53-56, use the properties of limits...Ch. 14.2 - In problems 53-56, use the properties of limits...Ch. 14.2 - In problems 53-56, use the properties of limits...Ch. 14.2 - Problems 57-60 are based on material learned...Ch. 14.2 - Problems 57-60 are based on material learned...Ch. 14.2 - Problems 57-60 are based on material learned...Ch. 14.2 - Problems 57-60 are based on material learned...Ch. 14.3 - For the function f( x )={ x 2 ifx0 x+1if0x2...Ch. 14.3 - What are the domain and range of f( x )=lnx ?Ch. 14.3 - True or False The exponential function f( x )= e x...Ch. 14.3 - Name the trigonometric functions that have...Ch. 14.3 - True or False Some rational functions have holes...Ch. 14.3 - True or False Every polynomial function has a...Ch. 14.3 - In Problems 7-42, find each limit algebraically....Ch. 14.3 - In Problems 7-42, find each limit algebraically....Ch. 14.3 - In Problems 7-42, find each limit algebraically....Ch. 14.3 - In Problems 7-42, find each limit algebraically....Ch. 14.3 - In Problems 7-42, find each limit algebraically....Ch. 14.3 - In Problems 7-42, find each limit algebraically....Ch. 14.3 - In Problems 7-42, find each limit algebraically....Ch. 14.3 - In Problems 7-42, find each limit algebraically....Ch. 14.3 - In Problems 7-42, find each limit algebraically....Ch. 14.3 - In Problems 7-42, find each limit algebraically....Ch. 14.3 - In Problems 7-42, find each limit algebraically....Ch. 14.3 - In Problems 7-42, find each limit algebraically....Ch. 14.3 - In Problems 7-42, find each limit algebraically....Ch. 14.3 - In Problems 7-42, find each limit algebraically....Ch. 14.3 - Find lim x 4 f( x ) .Ch. 14.3 - Find lim x 4 + f( x ) .Ch. 14.3 - Find lim x 2 f( x ) .Ch. 14.3 - Find lim x 2 + f( x ) .Ch. 14.3 - Does lim x4 f( x ) exist? If it does, what is it?Ch. 14.3 - Does lim x0 f( x ) exist? If it does, what is it?Ch. 14.3 - Is f continuous at 4 ?Ch. 14.3 - Is f continuous at 6 ?Ch. 14.3 - Is f continuous at 0?Ch. 14.3 - Is f continuous at 2?Ch. 14.3 - Is f continuous at 4?Ch. 14.3 - Is f continuous at 5?Ch. 14.3 - lim x 1 + ( 2x+3 )Ch. 14.3 - lim x 2 ( 42x )Ch. 14.3 - lim x 1 ( 2 x 3 +5x )Ch. 14.3 - lim x 2 + ( 3 x 2 8 )Ch. 14.3 - lim x/ 2 + sinxCh. 14.3 - lim x ( 3cosx )Ch. 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 - lim x 0 + x 3 x 2 x 4 + x 2Ch. 14.3 - lim x 2 + x 2 +x2 x 2 +2xCh. 14.3 - lim x 4 x 2 +x12 x 2 +4xCh. 14.3 - f( x )= x 3 3 x 2 +2x6c=2Ch. 14.3 - f( x )=3 x 2 6x+5c=3Ch. 14.3 - f( x )= x 2 +5 x6 c=3Ch. 14.3 - f( x )= x 3 8 x 2 +4 c=2Ch. 14.3 - f( x )= x+3 x3 c=3Ch. 14.3 - f( x )= x6 x+6 c=6Ch. 14.3 - f( x )= x 3 +3x x 2 3x c=0Ch. 14.3 - f( x )= x 2 6x x 2 +6x c=0Ch. 14.3 - f( x )={ x 3 +3x x 2 3x ifx0 1ifx=0 c=0Ch. 14.3 - f( x )={ x 2 6x x 2 +6x ifx0 2ifx=0 c=0Ch. 14.3 - f( x )={ x 3 +3x x 2 3x ifx0 1ifx=0 c=0Ch. 14.3 - f( x )={ x 2 6x x 2 +6x ifx0 1ifx=0 c=0Ch. 14.3 - f( x )={ x 3 1 x 2 1 ifx1 2ifx=1 3 x+1 ifx1 c=1Ch. 14.3 - f( x )={ x 2 2x x2 ifx2 2ifx=2 x4 x1 ifx2 c=2Ch. 14.3 - f( x )={ 2 e x ifx0 2ifx=0 x 3 +2 x 2 x 2 ifx0 c=0Ch. 14.3 - f( x )={ 3cosxifx0 3ifx=0 x 3 +3 x 2 x 2 ifx0 c=0Ch. 14.3 - f( x )=2x+3Ch. 14.3 - f( x )=43xCh. 14.3 - f( x )=3 x 2 +xCh. 14.3 - f( x )=3 x 3 +7Ch. 14.3 - f( x )=4sinxCh. 14.3 - f( x )=2cosxCh. 14.3 - f( x )=2tanxCh. 14.3 - f( x )=4cscxCh. 14.3 - f( x )= 2x+5 x 2 4Ch. 14.3 - f( x )= x 2 4 x 2 9Ch. 14.3 - f( x )= x3 InxCh. 14.3 - f( x )= lnx x3Ch. 14.3 - R( x )= x1 x 2 1 , c=1 and c=1Ch. 14.3 - R( x )= 3x+6 x 2 4 , c=2 and c=2Ch. 14.3 - R( x )= x 2 +x x 2 1 , c=1 and c=1Ch. 14.3 - R( x )= x 2 +4x x 2 16 , c=4 and c=4Ch. 14.3 - R( x )= x 3 x 2 +x1 x 4 x 3 +2x2Ch. 14.3 - R( x )= x 3 + x 2 +3x+3 x 4 + x 3 +2x+2Ch. 14.3 - R( x )= x 3 2 x 2 +4x8 x 2 +x6Ch. 14.3 - R( x )= x 3 x 2 +3x3 x 2 +3x4Ch. 14.3 - R( x )= x 3 +2 x 2 +x x 4 + x 3 +2x+2Ch. 14.3 - R( x )= x 3 3 x 2 +4x12 x 4 3 x 3 +x3Ch. 14.3 - R( x )= x 3 x 2 +x1 x 4 x 3 +2x2 Graph R(x) .Ch. 14.3 - R( x )= x 3 + x 2 +3x+3 x 4 + x 3 +2x+2 Graph R( x...Ch. 14.3 - R(x)= ( x 3 2 x 2 +4x8) ( x 2 +x6) Graph R( x ) .Ch. 14.3 - Prob. 86SBCh. 14.3 - Prob. 87SBCh. 14.3 - Prob. 88SBCh. 14.3 - Prob. 89DWCh. 14.3 - Prob. 90DWCh. 14.3 - Prob. 91RYKCh. 14.3 - Evaluate the permutation P( 5,3 ) .Ch. 14.3 - Prob. 93RYKCh. 14.3 - Prob. 94RYKCh. 14.4 - Find an equation of the line with slope 5...Ch. 14.4 - Prob. 2AYPCh. 14.4 - Prob. 3CVCh. 14.4 - Prob. 4CVCh. 14.4 - Prob. 5CVCh. 14.4 - Prob. 6CVCh. 14.4 - Prob. 7CVCh. 14.4 - Prob. 8CVCh. 14.4 - Prob. 9SBCh. 14.4 - Prob. 10SBCh. 14.4 - Prob. 11SBCh. 14.4 - Prob. 12SBCh. 14.4 - Prob. 13SBCh. 14.4 - Prob. 14SBCh. 14.4 - Prob. 15SBCh. 14.4 - Prob. 16SBCh. 14.4 - Prob. 17SBCh. 14.4 - Prob. 18SBCh. 14.4 - Prob. 19SBCh. 14.4 - Prob. 20SBCh. 14.4 - Prob. 21SBCh. 14.4 - Prob. 22SBCh. 14.4 - Prob. 23SBCh. 14.4 - Prob. 24SBCh. 14.4 - Prob. 25SBCh. 14.4 - Prob. 26SBCh. 14.4 - Prob. 27SBCh. 14.4 - Prob. 28SBCh. 14.4 - Prob. 29SBCh. 14.4 - Prob. 30SBCh. 14.4 - Prob. 31SBCh. 14.4 - f( x )=cosx at 0Ch. 14.4 - Prob. 33SBCh. 14.4 - Prob. 34SBCh. 14.4 - Prob. 35SBCh. 14.4 - Prob. 36SBCh. 14.4 - Prob. 37SBCh. 14.4 - Prob. 38SBCh. 14.4 - Prob. 39SBCh. 14.4 - Prob. 40SBCh. 14.4 - Prob. 41SBCh. 14.4 - Prob. 42SBCh. 14.4 - Prob. 43AECh. 14.4 - Prob. 44AECh. 14.4 - Prob. 45AECh. 14.4 - Prob. 46AECh. 14.4 - Prob. 47AECh. 14.4 - Instantaneous Velocity of a Ball In physics it is...Ch. 14.4 - Instantaneous Velocity on the Moon Neil Armstrong...Ch. 14.4 - Instantaneous Rate of Change The following data...Ch. 14.4 - Prob. 51RYKCh. 14.4 - Prob. 52RYKCh. 14.4 - Prob. 53RYKCh. 14.4 - Prob. 54RYKCh. 14.5 - In Problems 29-32, find the first five terms in...Ch. 14.5 - Prob. 2AYPCh. 14.5 - Prob. 3CVCh. 14.5 - Prob. 4CVCh. 14.5 - Prob. 5SBCh. 14.5 - Prob. 6SBCh. 14.5 - Prob. 7SBCh. 14.5 - Prob. 8SBCh. 14.5 - Prob. 9SBCh. 14.5 - Repeat Problem 9 for f( x )=4x .Ch. 14.5 - Prob. 11SBCh. 14.5 - Prob. 12SBCh. 14.5 - Prob. 13SBCh. 14.5 - Prob. 14SBCh. 14.5 - Prob. 15SBCh. 14.5 - Prob. 16SBCh. 14.5 - Prob. 17SBCh. 14.5 - Prob. 18SBCh. 14.5 - Prob. 19SBCh. 14.5 - Prob. 20SBCh. 14.5 - Prob. 21SBCh. 14.5 - Prob. 22SBCh. 14.5 - Prob. 23SBCh. 14.5 - Prob. 24SBCh. 14.5 - Prob. 25SBCh. 14.5 - Prob. 26SBCh. 14.5 - Prob. 27SBCh. 14.5 - Prob. 28SBCh. 14.5 - Prob. 29SBCh. 14.5 - Prob. 30SBCh. 14.5 - Prob. 31SBCh. 14.5 - Consider the function f( x )= 1 x 2 whose domain...Ch. 14.5 - Graph the function f( x )= log 2 x .Ch. 14.5 - If A=[ 1 2 3 4 ] and B=[ 5 6 0 7 8 1 ] , find AB .Ch. 14.5 - If f( x )=2 x 2 +3x+1 , find f( x+h )f( x ) h and...Ch. 14.5 - Prob. 36RYK
Additional Math Textbook Solutions
Find more solutions based on key concepts
Critical Values. In Exercises 41–44, find the indicated critical value. Round results to two decimal places.
42...
Elementary Statistics (13th Edition)
Student Ages The mean age of all 2550 students at a small college is 22.8 years with a standard deviation is 3....
Introductory Statistics
whether the pair of ratios forms a proportion.
Pre-Algebra Student Edition
In Exercises 9-22, change the Cartesian integral into an equivalent polar integral. Then evaluate the polar int...
University Calculus: Early Transcendentals (4th Edition)
Two symmetric dice have had two of their sides painted red, two painted black, one painted yellow, and the othe...
A First Course in Probability (10th Edition)
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.Similar questions
- Evaluate the integral using integration by parts. Sx² cos (9x) dxarrow_forwardLet 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. Need Help? Read It Master Itarrow_forwardVelocity of a Ball Thrown into the Air The position function of an object moving along a straight line is given by s = f(t). The average velocity of the object over the time interval [a, b] is the average rate of change of f over [a, b]; its (instantaneous) velocity at t = a is the rate of change of f at a. A ball is thrown straight up with an initial velocity of 128 ft/sec, so that its height (in feet) after t sec is given by s = f(t) = 128t - 16t². (a) What is the average velocity of the ball over the following time intervals? [3,4] [3, 3.5] [3, 3.1] ft/sec ft/sec ft/sec (b) What is the instantaneous velocity at time t = 3? ft/sec (c) What is the instantaneous velocity at time t = 7? ft/sec Is the ball rising or falling at this time? O rising falling (d) When will the ball hit the ground? t = sec Need Help? Read It Watch Itarrow_forward
- Find the slope of the tangent line to the graph of the function at the given point. f(x) = -4x + 5 at (-1, 9) m Determine an equation of the tangent line. y = Need Help? Read It Watch It SUBMIT ANSWERarrow_forwardFind the slope of the tangent line to the graph of the function at the given point. f(x) = 5x-4x² at (-1, -9) m Determine an equation of the tangent line. y = Need Help? Read It Master It SUBMIT ANSWERarrow_forwardFor what value of A and B the function f(x) will be continuous everywhere for the given definition?..arrow_forward
- 2. [-/1 Points] DETAILS MY NOTES SESSCALCET2 6.4.006.MI. Use the Table of Integrals to evaluate the integral. (Remember to use absolute values where appropriate. Use C for the constant of integration.) 7y2 y² 11 dy Need Help? Read It Master It SUBMIT ANSWER 3. [-/1 Points] DETAILS MY NOTES SESSCALCET2 6.4.009. Use the Table of Integrals to evaluate the integral. (Remember to use absolute values where appropriate. Use C for the constant of integration.) tan³(12/z) dz Need Help? Read It Watch It SUBMIT ANSWER 4. [-/1 Points] DETAILS MY NOTES SESSCALCET2 6.4.014. Use the Table of Integrals to evaluate the integral. (Use C for the constant of integration.) 5 sinб12x dx Need Help? Read Itarrow_forwardPlease refer belowarrow_forwardy"-9y+20y= 80t-156 y(0) = −6, y'(0) = 5 y(t) =arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
Algebra: Structure And Method, Book 1AlgebraISBN:9780395977224Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. ColePublisher:McDougal Littell
Algebra: Structure And Method, Book 1
Algebra
ISBN:9780395977224
Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:McDougal Littell
Limits and Continuity; Author: The Organic Chemistry Tutor;https://www.youtube.com/watch?v=9brk313DjV8;License: Standard YouTube License, CC-BY