Use the definition of continuity and the properties of limits to show that the function is continuous at the given number a. lim f(x) x--1 = F(x) = (x+4x³)*, lim x--1 = (lim a = -1 = lim (x) + lim x--1 = (lim (x) + ( [ = ([ 1))* lim -1 by the power law by the sum law 1 (x³)* by the multiple constant law by the direct substitution property Find f(-1). 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. lim f(x) x--1 = F(x) = (x+4x³)*, lim x--1 = (lim a = -1 = lim (x) + lim x--1 = (lim (x) + ( [ = ([ 1))* lim -1 by the power law by the sum law 1 (x³)* by the multiple constant law by the direct substitution property Find f(-1). f(-1) = Thus, by the definition of continuity, f is continuous at a = −1.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter4: Polynomial And Rational Functions
Section: Chapter Questions
Problem 15T
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![Use the definition of continuity and the properties of limits to show that the function is continuous at the given number a.
lim f(x)
x--1
=
F(x) = (x+4x³)*,
lim
x--1
= (lim
a = -1
=
lim (x) + lim
x--1
= (lim (x) + ( [
=
([
1))*
lim
-1
by the power law
by the sum law
1 (x³)* by the multiple constant law
by the direct substitution property
Find f(-1).
f(-1) =
Thus, by the definition of continuity, f is continuous at a = −1.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb6a0ed01-dc7e-4fee-9bdd-27c695376c3b%2Fc3708d65-6651-4351-8264-a489ec314de6%2Fgon2u2b_processed.png&w=3840&q=75)
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.
lim f(x)
x--1
=
F(x) = (x+4x³)*,
lim
x--1
= (lim
a = -1
=
lim (x) + lim
x--1
= (lim (x) + ( [
=
([
1))*
lim
-1
by the power law
by the sum law
1 (x³)* by the multiple constant law
by the direct substitution property
Find f(-1).
f(-1) =
Thus, by the definition of continuity, f is continuous at a = −1.
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