Short Answer

For each limit $\underset{x \to c}{l i m} f (x) = L$ in Exercises 43–54, use graphs and algebra to approximate the largest value of $δ$ such that if $x \in (c - δ, c) \cup (c, c + δ) then f (x) \in (L - ε, L + ε)$
$\underset{x \to - 1}{l i m} \frac{x^{2} - 2 x - 3}{x + 1} = - 4, ε = 0.1$

The required value of $δ = 0.1$

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1. Given Information

The given expression is $\underset{x \to - 1}{l i m} \frac{x^{2} - 2 x - 3}{x + 1} = - 4, ε = 0.1$

Step 2. Explanation

From the given expression, we have, $c = - 1, L = - 4$

The limit expression can be written as a formal statement as below,

For all epsilon positive, there exists a delta positive such that if $x \in (- 1 - δ, - 1) \cup (- 1, - 1 + δ) Then \frac{x^{2} - 2 x - 3}{x + 1} \in (- 4 - ε, - 4 + ε)$

Now, the largest value of delta is given by,

$\frac{x^{2} - 2 x - 3}{x + 1} = L + ε \frac{x^{2} - 2 x - 3}{x + 1} = - 4 + 1 x - 3 = - 3 x = 0$

Thus,

$δ = 0 + 0.1 δ = 0.1$

Find Study Materials for

Create Study Materials

Select your language

Calculus

Answers without the blur.

Short Answer

For each limit $\underset{x \to c}{l i m} f (x) = L$ in Exercises 43–54, use graphs and algebra to approximate the largest value of $δ$ such that if $x \in (c - δ, c) \cup (c, c + δ) then f (x) \in (L - ε, L + ε)$
$\underset{x \to - 1}{l i m} \frac{x^{2} - 2 x - 3}{x + 1} = - 4, ε = 0.1$

Step by Step Solution

Step 1. Given Information

Step 2. Explanation

Most popular questions for Math Textbooks

Want to see more solutions like these?

Recommended explanations on Math Textbooks

Select your language

Calculus

Answers without the blur.

Short Answer

For each limit limx→cf(x)=Lin Exercises 43–54, use graphs and algebra to approximate the largest value of δ such that if x∈(c-δ,c)∪(c,c+δ) then f(x)∈(L-ε,L+ε) limx→-1x2-2x-3x+1=-4,ε=0.1

Step by Step Solution

Step 1. Given Information

Step 2. Explanation

Most popular questions for Math Textbooks

Want to see more solutions like these?

Recommended explanations on Math Textbooks

Decision Maths

Calculus

Probability and Statistics

Statistics

Mechanics Maths

Geometry

Pure Maths

For each limit $\underset{x \to c}{l i m} f (x) = L$ in Exercises 43–54, use graphs and algebra to approximate the largest value of $δ$ such that if $x \in (c - δ, c) \cup (c, c + δ) then f (x) \in (L - ε, L + ε)$
$\underset{x \to - 1}{l i m} \frac{x^{2} - 2 x - 3}{x + 1} = - 4, ε = 0.1$