If lim f(x) = 5, must f be defined at x = 1? If it is, must f(1) = 5? Can anything be concluded about the values of f at x = 1? Explain. X-1 Must f be defined at x= 1? Yes No If f is defined at x = 1, must f(1) = 5? O A. No, because even if a function is defined at a particular point, it may not exist at that point. O B. Yes, because if it is defined at x = 1, the f(1) must equal lim f(x). X-1 OC. No, because it might be a piecewise function where the limit approaching 1 from the left and the limit approaching 1 from the right are the same, but f(1) might be defined as a different value. Can anything be concluded about the values of f at x = 1? OA. No, nothing can be concluded without knowing more about the definition of f. O B. Yes, f(1) must equal 5.

Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter3: The Derivative
Section3.CR: Chapter 3 Review
Problem 2CR
icon
Related questions
Question

How is the conclusion for part a found?

If lim f(x) = 5, must f be defined at x = 1? If it is, must f(1) = 5? Can anything be concluded about the values of f at x = 1? Explain.
X→1
Must f be defined at x = 1?
Yes
No
If f is defined at x= 1, must f(1) = 5?
A. No, because even if a function is defined at a particular point, it may not exist at that point.
B. Yes, because if it is defined at x = 1, the f(1) must equal lim f(x).
X→1
C. No, because it might be a piecewise function where the limit approaching 1 from the left and the limit approaching 1 from the right are the same, but f(1) might be defined as a different value.
Can anything be concluded about the values of f at x = 1?
A. No, nothing can be concluded without knowing more about the definition of f.
B. Yes, f(1) must equal 5.
Transcribed Image Text:If lim f(x) = 5, must f be defined at x = 1? If it is, must f(1) = 5? Can anything be concluded about the values of f at x = 1? Explain. X→1 Must f be defined at x = 1? Yes No If f is defined at x= 1, must f(1) = 5? A. No, because even if a function is defined at a particular point, it may not exist at that point. B. Yes, because if it is defined at x = 1, the f(1) must equal lim f(x). X→1 C. No, because it might be a piecewise function where the limit approaching 1 from the left and the limit approaching 1 from the right are the same, but f(1) might be defined as a different value. Can anything be concluded about the values of f at x = 1? A. No, nothing can be concluded without knowing more about the definition of f. B. Yes, f(1) must equal 5.
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 2 steps with 2 images

Blurred answer
Recommended textbooks for you
Calculus For The Life Sciences
Calculus For The Life Sciences
Calculus
ISBN:
9780321964038
Author:
GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:
Pearson Addison Wesley,
College Algebra
College Algebra
Algebra
ISBN:
9781938168383
Author:
Jay Abramson
Publisher:
OpenStax
Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage