
Concept explainers
The limit of the expression

Answer to Problem 1RE
Solution:
The value of the expression
Explanation of Solution
Given Information:
Consider the provided function is
Consider the provided expression is
As
Construct a table representing the number that the corresponding values of
Choose values of
Take
and find the corresponding value of
Thus,
Choose an additional value of
Take
and find the corresponding value of
Thus,
Choose an additional value of
Take
and find the corresponding value of
Thus,
List the values of
0.99 | 2.9701 |
0.999 | 2.997001 |
0.9999 | 2.99970001 |
From the above table, it is clear that, as
Now choose values of
Take
and find the corresponding value of
Thus,
Choose an additional number of
Take
and find the corresponding value of
Thus,
Again, select an additional number of
Take
and find the corresponding value of
Thus,
List the values of
1.01 | 3.0301 |
1.001 | 3.003001 |
1.0001 | 3.00030001 |
From the above table, it is clear that, as
Combine both the tables as follows:
0.99 | 2.9701 | 3.0301 | 0.99 |
0.999 | 2.997001 | 3.003001 | 0.999 |
0.9999 | 2.99970001 | 3.00030001 | 0.9999 |
The tables show the values of
Thus as
get closer to 3.
Therefore,
Want to see more full solutions like this?
Chapter 11 Solutions
Precalculus (6th Edition)
- A Content X MindTap - Cengage Learning x Function Evaluations x + /ui/evo/index.html?elSBN=9780357038406&id=339416021&snapshotld=877369& GE MINDTAP , Limits, and the Derivative ⭑ វា a ANSWEI 16. Refer to the graph of the function f in the following figure. कर्ट AA C 54 -3-2 7 7 Ay 6. S 5. y=f(x) 4 3. 2. 1 -3- 34567 8 00 9 10 a. Find the value of ƒ (7). b. Find the values of x corresponding to the point(s) on the graph of ƒ located at a height of 5 units from the x-axis. c. Find the point on the x-axis at which the graph of ƒ crosses it. What is the value of f (x) at this point? d. Find the domain and range of f. MacBook Pro G Search or type URL + > % Λ & 5 6 7 29 ( 8 9 0arrow_forwardMorgan F. - C X A Courses MindTap - Cengage Learning Х Domain of Square Roots X + gage.com/static/nb/ui/evo/index.html?elSBN 9780357038406&id=339416021&snapshotld=877369& CENGAGE MINDTAP 2: Functions, Limits, and the Derivative 47. x if x < 0 f(x) = 2x+1 if x 0 Answerarrow_forwardA Content MindTap - Cengage Learning × Function Evaluations * + c/nb/ui/evo/index.html?elSBN 9780357038406&id=339416021&snapshotld=877369& GAGE MINDTAP ions, Limits, and the Derivative 15. Refer to the graph of the function f in the following figure. 6 y = f(x) 5 4+ 3- 2- 1 + 2 -1 3 4 5 6 a. Find the value of ƒ (0). Answer-> b. Find the value of x for which (i) f (x) = 3 and (ii) f (x) = 0. Answer ▾ c. Find the domain of f. Answer + d. Find the range of f. Answer+ MacBook Proarrow_forward
- Answer-> 12. Let g be the function defined by Find g(-2), g(0), g (2), and g (4). - +1 if x <2 g(x) = √√√x-2 if x 2arrow_forward13. Let f be the function defined by Find f (-1), f (0), ƒ (1) and ƒ (2). Answer f(x) = .2 J-x² +3 if x <1 2x²+1 2x²+1 if x ≥ 1arrow_forwardΛ Content Mind Tap - Cengage Learning × Function Evaluations x + c/nb/ui/evo/index.html?elSBN 9780357038406&id=339416021&snapshotld=877369& GAGE MINDTAP ons, Limits, and the Derivative 14. Let f be the function defined by Find f (0), f (1), and f (2). 2+1 x if x 1 if x 1 f(x) = 1 1-xarrow_forward
- A Content c/nb/ui/evo/index.html?elSBN 9780357038406&id=339416021&snapshotld=877369& GAGE MINDTAP ons, Limits, and the Derivative 11. Let f be the function defined by Find f (-2), f (0), and f (1). Answer f(x) = [ x² + 1 if x ≤ 0 if x > 0arrow_forwardGiven that 4−4i is a zero, factor the following polynomial function completely. Use the Conjugate Roots Theorem, if applicable. f(x)=x4−5x3−2x2+176x−320arrow_forwardeliminate the parameter to find the cartesian equation of the curve and sketch the graph. On the graph show the direction it takes and the initial and terminal point. Please draw by hand and show how you got to each steparrow_forward
- eliminate the parameter to find the cartesian equation of the curve and sketch the graph. On the graph show the direction it takes and the initial and terminal point. Please draw by hand and show how you got to each steparrow_forwardeliminate the parameter to find the cartesian equation of the curve and sketch the graph. On the graph show the direction it takes and the initial and terminal point. Please draw by hand and show how you got to each steparrow_forwardeliminate the parameter to find the cartesian equation of the curve and sketch the graph. On the graph show the direction it takes and the initial and terminal point. Please draw by hand and show how you got to each steparrow_forward
- Calculus: Early TranscendentalsCalculusISBN:9781285741550Author:James StewartPublisher:Cengage LearningThomas' Calculus (14th Edition)CalculusISBN:9780134438986Author:Joel R. Hass, Christopher E. Heil, Maurice D. WeirPublisher:PEARSONCalculus: Early Transcendentals (3rd Edition)CalculusISBN:9780134763644Author:William L. Briggs, Lyle Cochran, Bernard Gillett, Eric SchulzPublisher:PEARSON
- Calculus: Early TranscendentalsCalculusISBN:9781319050740Author:Jon Rogawski, Colin Adams, Robert FranzosaPublisher:W. H. FreemanCalculus: Early Transcendental FunctionsCalculusISBN:9781337552516Author:Ron Larson, Bruce H. EdwardsPublisher:Cengage Learning





