Chapter 1: Q. 61 (page 108)

For each of the limit statements in Exercises 61-66, write a $δ - M, N - ϵ$ , or $N - M$ proof, according to the type of limit statement.
$\lim_{x \to - 2^{+}} \frac{1}{x + 2} = \infty$

Short Answer

Expert verified

Delta-epsilon proof is,

$δ = \frac{1}{M}$

Step by step solution

Step 1. Given information

We are given,

$\lim_{x \to - 2^{+}} \frac{1}{x + 2} = \infty$

Step 2. Writing the delta-epsilon proofs

The strategy is to use algebra to find $δ$ in terms of M,

From the given limit, we get

$f (x) = \frac{1}{x + 2} c = - 2 L = \infty$

Given $M > 0$ , choose $δ = \frac{1}{M}$ .

If $x \in (- 2, - 2 + δ)$ , we have $0 < x + 2 < δ$ ,

Now for $δ > 0$ ,

role="math" $| x - (- 2) | < δ | x + 2 | < δ \frac{1}{| x + 2 |} < \frac{1}{δ} < M$

Hence,

$δ = \frac{1}{M}$

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For each of the limit statements in Exercises 61-66, write a $δ - M, N - ϵ$ , or $N - M$ proof, according to the type of limit statement.
$\lim_{x \to - 2^{+}} \frac{1}{x + 2} = \infty$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Writing the delta-epsilon proofs

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For each of the limit statements in Exercises 61-66, write a δ-M,N-ϵ, or N-Mproof, according to the type of limit statement.limx→-2+1x+2=∞

Short Answer

Step by step solution

Step 1. Given information

Step 2. Writing the delta-epsilon proofs

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Mechanics Maths

Theoretical and Mathematical Physics

Decision Maths

Pure Maths

Logic and Functions

Discrete Mathematics

Study anywhere. Anytime. Across all devices.

For each of the limit statements in Exercises 61-66, write a $δ - M, N - ϵ$ , or $N - M$ proof, according to the type of limit statement.
$\lim_{x \to - 2^{+}} \frac{1}{x + 2} = \infty$