Chapter 1: Q. 65 (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.
$\lim_{x \to \infty} (3 x - 5) = \infty$

Short Answer

Expert verified

The proof of given limit $\lim_{x \to \infty} (3 x - 5) = \infty$ is,

$N = \frac{M + 5}{3}$

Step by step solution

Step 1. Given information

We are given,

$\lim_{x \to \infty} (3 x - 5) = \infty$

Step 2. Writing the proofs

The strategy is to use algebra to findN in terms of M,

From the given limit, we get

$f (x) = 3 x - 5 L = \infty c = \infty$

Given $M > 0$ , choose $N = \frac{M + 5}{3}$ .

If $x > N$ , we have,

$3 x - 5 > 3 N - 5 = M$

So,

$3 N - 5 = M 3 N = M + 5 N = \frac{M + 5}{3}$

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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.
$\lim_{x \to \infty} (3 x - 5) = \infty$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Writing the proofs

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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.limx→∞(3x-5)=∞

Short Answer

Step by step solution

Step 1. Given information

Step 2. Writing the proofs

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Logic and Functions

Decision Maths

Theoretical and Mathematical Physics

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Statistics

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.
$\lim_{x \to \infty} (3 x - 5) = \infty$