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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.

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
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter4: Polynomial And Rational Functions
Section4.5: Rational Functions
Problem 54E
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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.
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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