Use the definition of continuity and the properties of limits to show that the function is continuous at the given number a. f(x) = (x + 2x³) ², lim_ f(x) X→-1 lim X→-1 = lim x + X→-1 - (lim = (-₁ + ² ( [ 1 = || a = -1 4 4 ²+³) ² +3 lim X→-1 4 D) f(-1) = Thus, by the definition of continuity, f is continuous at a = -1.
Use the definition of continuity and the properties of limits to show that the function is continuous at the given number a. f(x) = (x + 2x³) ², lim_ f(x) X→-1 lim X→-1 = lim x + X→-1 - (lim = (-₁ + ² ( [ 1 = || a = -1 4 4 ²+³) ² +3 lim X→-1 4 D) f(-1) = Thus, by the definition of continuity, f is continuous at a = -1.
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
Related questions
Question
2.4 Q5
Transcribed Image Text:Use the definition of continuity and the properties of limits to show that the function is continuous at the given number a.
f(x) = (x + 2x³) ²,
lim_ f(x)
X→-1
=
=
-
lim
X→-1
||
lim x +
X→-1
= (-₁ + ² ( [
1
a = -1
4
4
²+³) ²
+3
lim
X→-1
4
D)
f(-1) =
Thus, by the definition of continuity, f is continuous at a = -1.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 3 steps with 3 images
Recommended textbooks for you
Calculus: Early Transcendentals
Calculus
ISBN:
9781285741550
Author:
James Stewart
Publisher:
Cengage Learning
Thomas' Calculus (14th Edition)
Calculus
ISBN:
9780134438986
Author:
Joel R. Hass, Christopher E. Heil, Maurice D. Weir
Publisher:
PEARSON
Calculus: Early Transcendentals (3rd Edition)
Calculus
ISBN:
9780134763644
Author:
William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:
PEARSON
Calculus: Early Transcendentals
Calculus
ISBN:
9781285741550
Author:
James Stewart
Publisher:
Cengage Learning
Thomas' Calculus (14th Edition)
Calculus
ISBN:
9780134438986
Author:
Joel R. Hass, Christopher E. Heil, Maurice D. Weir
Publisher:
PEARSON
Calculus: Early Transcendentals (3rd Edition)
Calculus
ISBN:
9780134763644
Author:
William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:
PEARSON
Calculus: Early Transcendentals
Calculus
ISBN:
9781319050740
Author:
Jon Rogawski, Colin Adams, Robert Franzosa
Publisher:
W. H. Freeman
Calculus: Early Transcendental Functions
Calculus
ISBN:
9781337552516
Author:
Ron Larson, Bruce H. Edwards
Publisher:
Cengage Learning