Precalculus: Mathematics for Calculus (Standalone Book)
7th Edition
ISBN: 9781305071759
Author: James Stewart, Lothar Redlin, Saleem Watson
Publisher: Brooks Cole
expand_more
expand_more
format_list_bulleted
Concept explainers
Videos
Textbook Question
Chapter 13.1, Problem 1E
When we write
Expert Solution & Answer
Trending nowThis is a popular solution!
Students have asked these similar questions
Evaluate the limit: lim h→0 (6 + h)-1 − 6-1 / h
*I'm not sure how to solve when I have an exponent of -1*
EXAMPLE 3 Evaluate the limit below and indicate which properties of limits are used at each stage.
lim x → ∞
5x2 − 5x − 2/
4x2 + 3x + 1
SOLUTION As x becomes large, both numerator and denominator become large, so it isn't obvious what happens to their ratio. We need to do some preliminary algebra.To evaluate the limit at infinity of any rational function, we first divide both numerator and denominator by the highest power of x that occurs in the denominator. (We may assume that
x ≠ 0,
since we are interested only in large values of x.) In this case the highest power of x in the denominator is
x2,
so we have
lim x → ∞
5x2 − 5x − 2/
4x2 + 3x + 1
=
lim x → ∞
5x2 − 5x − 2/x2
4x2 + 3x + 1/x2
=
lim x → ∞
5 −
5/x
−
2/x2
4 +
3/x
+
1/x2
=
lim x → ∞
5 −
5/x
−
2/x2
lim x → ∞
4 +
3/x
+
1/x2…
Let (x) = |x - 2| / x - 2
A) what is the domain of g(x)?
B) Use numerical methods to find lim x—> 2- g(x) and lim x—> 2+ g(x).
C) based on your answer to (b), what is lim x—> 2 g(x)?
D) sketch an accurate graph of g(x) on the interval [-4,4]. Be sure to include any needed open or closed circles.
Chapter 13 Solutions
Precalculus: Mathematics for Calculus (Standalone Book)
Ch. 13.1 - When we write limxaf(x)=L then, roughly speaking,...Ch. 13.1 - We write limxaf(x)=L and say that the ______ of...Ch. 13.1 - Prob. 3ECh. 13.1 - Prob. 4ECh. 13.1 - Prob. 5ECh. 13.1 - Prob. 6ECh. 13.1 - Prob. 7ECh. 13.1 - Prob. 8ECh. 13.1 - Prob. 9ECh. 13.1 - Prob. 10E
Ch. 13.1 - Prob. 11ECh. 13.1 - Prob. 12ECh. 13.1 - Prob. 13ECh. 13.1 - Estimating Limits Numerically and Graphically Use...Ch. 13.1 - Prob. 15ECh. 13.1 - Prob. 16ECh. 13.1 - Prob. 17ECh. 13.1 - Limits from a Graph For the function f whose graph...Ch. 13.1 - Limits from a Graph For the function f whose graph...Ch. 13.1 - Limits from a Graph For the function f whose graph...Ch. 13.1 - Prob. 21ECh. 13.1 - Prob. 22ECh. 13.1 - Prob. 23ECh. 13.1 - Estimating Limits Graphically Use a graphing...Ch. 13.1 - Prob. 25ECh. 13.1 - Prob. 26ECh. 13.1 - Prob. 27ECh. 13.1 - Prob. 28ECh. 13.1 - Prob. 29ECh. 13.1 - One-Sided Limits Graph the piecewise-defined...Ch. 13.1 - Prob. 31ECh. 13.1 - Prob. 32ECh. 13.1 - Prob. 33ECh. 13.1 - DISCUSS: Graphing Calculator Pitfalls (a)...Ch. 13.2 - Suppose the following limits exist:...Ch. 13.2 - If f is a polynomial or a rational function and a...Ch. 13.2 - Limits from a Graph The graphs of f and g are...Ch. 13.2 - Prob. 4ECh. 13.2 - Using Limit Laws Evaluate the limit and justify...Ch. 13.2 - Prob. 6ECh. 13.2 - Prob. 7ECh. 13.2 - Prob. 8ECh. 13.2 - Prob. 9ECh. 13.2 - Prob. 10ECh. 13.2 - Prob. 11ECh. 13.2 - Prob. 12ECh. 13.2 - Prob. 13ECh. 13.2 - Prob. 14ECh. 13.2 - Prob. 15ECh. 13.2 - Prob. 16ECh. 13.2 - Prob. 17ECh. 13.2 - Using Limit Laws Evaluate the limit and justify...Ch. 13.2 - Prob. 19ECh. 13.2 - Prob. 20ECh. 13.2 - Prob. 21ECh. 13.2 - Prob. 22ECh. 13.2 - Prob. 23ECh. 13.2 - Prob. 24ECh. 13.2 - Prob. 25ECh. 13.2 - Prob. 26ECh. 13.2 - Prob. 27ECh. 13.2 - Prob. 28ECh. 13.2 - Prob. 29ECh. 13.2 - Prob. 30ECh. 13.2 - Prob. 31ECh. 13.2 - Prob. 32ECh. 13.2 - Prob. 33ECh. 13.2 - Prob. 34ECh. 13.2 - Prob. 35ECh. 13.2 - Prob. 36ECh. 13.2 - Prob. 37ECh. 13.2 - Prob. 38ECh. 13.2 - Prob. 39ECh. 13.2 - Prob. 40ECh. 13.2 - Does the Limit Exist? Find the limit, if it...Ch. 13.2 - Does the Limit Exist? Find the limit, if it...Ch. 13.2 - Does the Limit Exist? Let f(x)={x1ifx2x24x+6ifx2...Ch. 13.2 - Prob. 44ECh. 13.2 - Finding Limits Numerically and Graphically (a)...Ch. 13.2 - Prob. 46ECh. 13.2 - Prob. 47ECh. 13.2 - Prob. 48ECh. 13.2 - DISCUSS PROVE: Limits of Sums and Products (a)...Ch. 13.3 - The derivative of a function f at a number a is...Ch. 13.3 - Prob. 2ECh. 13.3 - Prob. 3ECh. 13.3 - Prob. 4ECh. 13.3 - Prob. 5ECh. 13.3 - Prob. 6ECh. 13.3 - Prob. 7ECh. 13.3 - Prob. 8ECh. 13.3 - Prob. 9ECh. 13.3 - Prob. 10ECh. 13.3 - Prob. 11ECh. 13.3 - Prob. 12ECh. 13.3 - Equation of a Tangent Line Find an equation of the...Ch. 13.3 - Prob. 14ECh. 13.3 - Prob. 15ECh. 13.3 - Prob. 16ECh. 13.3 - Prob. 17ECh. 13.3 - Prob. 18ECh. 13.3 - Prob. 19ECh. 13.3 - Prob. 20ECh. 13.3 - Prob. 21ECh. 13.3 - Prob. 22ECh. 13.3 - Prob. 23ECh. 13.3 - Prob. 24ECh. 13.3 - Prob. 25ECh. 13.3 - Prob. 26ECh. 13.3 - Prob. 27ECh. 13.3 - Prob. 28ECh. 13.3 - Prob. 29ECh. 13.3 - Prob. 30ECh. 13.3 - Prob. 31ECh. 13.3 - Tangent Lines (a) If g(x) = 1/(2x 1), find g(a)....Ch. 13.3 - Prob. 33ECh. 13.3 - Prob. 34ECh. 13.3 - Prob. 35ECh. 13.3 - Prob. 36ECh. 13.3 - Velocity of a Ball If a ball is thrown straight up...Ch. 13.3 - Velocity on the Moon If an arrow is shot upward on...Ch. 13.3 - Prob. 39ECh. 13.3 - Inflating a Balloon A spherical balloon is being...Ch. 13.3 - Temperature Change A roast turkey is taken from an...Ch. 13.3 - Heart Rate A cardiac monitor is used to measure...Ch. 13.3 - Prob. 43ECh. 13.3 - World Population Growth The table gives...Ch. 13.3 - Prob. 45ECh. 13.3 - Prob. 46ECh. 13.4 - Let f be a function defined on some interval (a,...Ch. 13.4 - Prob. 2ECh. 13.4 - Limits from a Graph (a) Use the graph of f to find...Ch. 13.4 - Prob. 4ECh. 13.4 - Prob. 5ECh. 13.4 - Prob. 6ECh. 13.4 - Prob. 7ECh. 13.4 - Prob. 8ECh. 13.4 - Prob. 9ECh. 13.4 - Prob. 10ECh. 13.4 - Prob. 11ECh. 13.4 - Prob. 12ECh. 13.4 - Prob. 13ECh. 13.4 - Prob. 14ECh. 13.4 - Prob. 15ECh. 13.4 - Prob. 16ECh. 13.4 - Limits at Infinity Find the limit. 17. limxcosxCh. 13.4 - Prob. 18ECh. 13.4 - Prob. 19ECh. 13.4 - Prob. 20ECh. 13.4 - Estimating Limits Numerically and Graphically Use...Ch. 13.4 - Prob. 22ECh. 13.4 - Prob. 23ECh. 13.4 - Prob. 24ECh. 13.4 - Prob. 25ECh. 13.4 - Prob. 26ECh. 13.4 - Prob. 27ECh. 13.4 - Prob. 28ECh. 13.4 - Prob. 29ECh. 13.4 - Prob. 30ECh. 13.4 - Prob. 31ECh. 13.4 - Prob. 32ECh. 13.4 - Prob. 33ECh. 13.4 - Prob. 34ECh. 13.4 - Prob. 35ECh. 13.4 - Prob. 36ECh. 13.4 - Prob. 37ECh. 13.4 - Prob. 38ECh. 13.4 - Salt Concentration (a) A tank contains 5000 L of...Ch. 13.4 - Velocity of a Raindrop The downward velocity of a...Ch. 13.4 - DISCUSS: The Limit of a Recursive Sequence (a) A...Ch. 13.5 - The graph of a function f is shown below. 1. To...Ch. 13.5 - Prob. 2ECh. 13.5 - Estimating an Area Using Rectangles (a) By reading...Ch. 13.5 - Prob. 4ECh. 13.5 - Prob. 5ECh. 13.5 - Prob. 6ECh. 13.5 - Prob. 7ECh. 13.5 - Prob. 8ECh. 13.5 - Prob. 9ECh. 13.5 - Estimating Areas Using Rectangles In these...Ch. 13.5 - Prob. 11ECh. 13.5 - Prob. 12ECh. 13.5 - Prob. 13ECh. 13.5 - Prob. 14ECh. 13.5 - Prob. 15ECh. 13.5 - Prob. 16ECh. 13.5 - Prob. 17ECh. 13.5 - Prob. 18ECh. 13.5 - Prob. 19ECh. 13.5 - Prob. 20ECh. 13.5 - Prob. 21ECh. 13.5 - Prob. 22ECh. 13 - (a) Explain what is meant by limxa f(x) = L. (b)...Ch. 13 - To evaluate the limit of a function, we often need...Ch. 13 - (a) Explain what it means to...Ch. 13 - (a) Define the derivative f(a) of a function f at...Ch. 13 - (a) Give two different interpretations of the...Ch. 13 - (a) Explain what is meant by limx f(x) = L. Draw...Ch. 13 - (a) If a1, a2, a3, is a sequence, what is meant...Ch. 13 - (a) Suppose S is the region under the graph of the...Ch. 13 - Estimating Limits Numerically and Graphically Use...Ch. 13 - Estimating Limits Numerically and Graphically Use...Ch. 13 - Estimating Limits Numerically and Graphically Use...Ch. 13 - Estimating Limits Numerically and Graphically Use...Ch. 13 - Estimating Limits Numerically and Graphically Use...Ch. 13 - Estimating Limits Numerically and Graphically Use...Ch. 13 - Limits from a Graph The graph of f is shown in the...Ch. 13 - One-Sided Limits Let f(x)={2ifx1x2if1x2x+2ifx2...Ch. 13 - Finding Limits Evaluate the limit, if it exists....Ch. 13 - Finding Limits Evaluate the limit, if it exists....Ch. 13 - Finding Limits Evaluate the limit, if it exists....Ch. 13 - Finding Limits Evaluate the limit, if it exists....Ch. 13 - Prob. 13RECh. 13 - Prob. 14RECh. 13 - Prob. 15RECh. 13 - Prob. 16RECh. 13 - Prob. 17RECh. 13 - Prob. 18RECh. 13 - Prob. 19RECh. 13 - Prob. 20RECh. 13 - Prob. 21RECh. 13 - Derivative of a Function Find the derivative of...Ch. 13 - Prob. 23RECh. 13 - Prob. 24RECh. 13 - Prob. 25RECh. 13 - Prob. 26RECh. 13 - Prob. 27RECh. 13 - Prob. 28RECh. 13 - Prob. 29RECh. 13 - Prob. 30RECh. 13 - Prob. 31RECh. 13 - Prob. 32RECh. 13 - Prob. 33RECh. 13 - Prob. 34RECh. 13 - Prob. 35RECh. 13 - Prob. 36RECh. 13 - Prob. 37RECh. 13 - Prob. 38RECh. 13 - Prob. 39RECh. 13 - Prob. 40RECh. 13 - Prob. 41RECh. 13 - Prob. 42RECh. 13 - Prob. 43RECh. 13 - Prob. 44RECh. 13 - Prob. 45RECh. 13 - Prob. 46RECh. 13 - Prob. 47RECh. 13 - Prob. 48RECh. 13 - Prob. 1TCh. 13 - For the piecewise-defined function f whose graph...Ch. 13 - Prob. 3TCh. 13 - Prob. 4TCh. 13 - Prob. 5TCh. 13 - Prob. 6TCh. 13 - Prob. 7TCh. 13 - Work Done by a Winch A motorized winch is being...Ch. 13 - Prob. 2PCh. 13 - Prob. 3PCh. 13 - Prob. 4PCh. 13 - Prob. 5P
Additional Math Textbook Solutions
Find more solutions based on key concepts
(a) If Fx is an antiderivative for fx , then abfxdx= (b) abFxdx= (c) ddxaxftdt=
Calculus Early Transcendentals, Binder Ready Version
Evaluate the integrals in Exercises 1–46.
1.
University Calculus: Early Transcendentals (3rd Edition)
147. Draining a tank Water drains from the conical tank shown in the accompanying figure at the rate .
a. What...
University Calculus: Early Transcendentals, Single Variable (3rd Edition)
the order of numbers from least to greatest.
Glencoe Math Accelerated, Student Edition
Evaluate the integrals in Exercises 1–46.
1.
University Calculus: Early Transcendentals (4th 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
- How do I find a limit in terms of constant a? lim ((2/a+h)-(2/a)) / h h->0arrow_forwardHow do I solve this problem below? I am currently researching limits in Calculus. Evaluate the Limit if it exists? lim x→25 5 − x 25x − x2 and lim h→0 (3 + h)3 − 27 harrow_forwardReferring to the graph of a function f given below, nd each limit. Evaluate the limit. lim x!1+ x2f(f(x)) (b) Evaluate the limit. lim xx2 + f(f(x))arrow_forward
- Fast pls solve this question correctly in 5 min pls i need urgently pls solve Nid Create a table of values for the function and use the result to estimate the limit, lim x-4 [1/(x+1)]-(1/5)/x-4arrow_forward(a) Use a graph of ______________ ______________f(x) = √3 x2 + 8x + 6 - √3 x2 + 3x + 1 to estimate the value of lim x->∞ f(x) to one decimalplace.(b) Use a table of values of f(x) to estimate the limit tofour decimal places.(c) Find the exact value of the limit.arrow_forwardConsider lim as given. (a) Use the definition of limits at infinity to find the value of M that corresponds to ε = 0.5. (b) Use the definition of limits at infinity to find the value of M that corresponds to ε = 0.1.arrow_forward
- Given lim (4x-3) as x approaches 1. Use the definition of a limt to find a number delta such that the absolute value of x-a is less than delta when the absolute value of f(x)-L is less than 0.08arrow_forward(a)Consider the following information. lim x→c f(x) = 4 lim x→c g(x) = 7/6 *lim x→c f(x)/g(x) (b) Find the limit. (If an answer does not exist, enter DNE.) lim x→1 (x2 + x − 2)/(x2 − 1) (c) Create a table of values for the function and use the result to estimate the limit. Use a graphing utility to graph the function to confirm your result. (Round your answers to four decimal places. If an answer does not exist, enter DNE.) lim x→−3 root of 46 − x-7/x+3 x −3.1 −3.01 −3.001 −2.999 −2.99 −2.9 f(x) lim x→−3 root of 46 − x-7/x+3 ≈arrow_forward(a ) find the limit. (If an answer does not exist, enter DNE.) lim x→0 x/x2+3x (b) Find the limit. (If an answer does not exist, enter DNE.) lim x→0 [1/(5 + x)] − (1/5)/x (c) Find the limit. (If an answer does not exist, enter DNE.) lim Δx→0 2(x + Δx) − 2x/Δx (d) Consider the following function. f(x) = 6x2 − 8x Find the limit. lim Δx→0 f(x+Δx) -f(x)/Δxarrow_forward
- Which of the following is/are signified by limx→af(x)=∞limx→af(x)=∞? The limit exists and equals infinity. The value of xx goes out to infinity, when it gets close to aa. This means that f(a)=∞f(a)=∞ As xx approaches aa, the value of f(x)f(x) increases without bound. The value of f(x)f(x) becomes infinite when xx approaches aa.arrow_forward5. Given the graph of g(x) = {√−x−2+1, x<-2 x2+2x+5, x≥-2 below, evaluate its limit as x approaches -2. a. 3 b. 1 c. the limit does not exist d. 5 6. Evaluate lim g(x) x→-3-. a. 18 b. - ∞ c.0 d. ∞ 7. Let g(x) = -1/x2. Evaluate lim g(x) x→0 by drawing its graph. a. ∞ b. 1 c. 0 d. -∞arrow_forward(a) Find the limit. (If an answer does not exist, enter DNE.) lim x→1 (x2 + x − 2)/(x2 − 1) (b) Create a table of values for the function and use the result to estimate the limit. Use a graphing utility to graph the function to confirm your result. (Round your answers to four decimal places. If an answer does not exist, enter DNE.) lim x→−3 Sq.Root 46 − x-7/x+3 x −3.1 −3.01 −3.001 −2.999 −2.99 −2.9 f(x) lim x→−3 Sq.Root 46 − x-7/x+3 ≈arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
Functions and Change: A Modeling Approach to Coll...AlgebraISBN:9781337111348Author:Bruce Crauder, Benny Evans, Alan NoellPublisher:Cengage Learning
Functions and Change: A Modeling Approach to Coll...
Algebra
ISBN:9781337111348
Author:Bruce Crauder, Benny Evans, Alan Noell
Publisher:Cengage Learning
Limits and Continuity; Author: The Organic Chemistry Tutor;https://www.youtube.com/watch?v=9brk313DjV8;License: Standard YouTube License, CC-BY