Chapter 1: Q. 66 (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 delta-epsilon proofs

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

From the given limit, we get

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

Glven $M < 0$ , choose $N = \frac{M + 5}{3}$ .

If role="math" localid="1648036421117" $x < N$ , 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 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-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 delta-epsilon proofs

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Probability and Statistics

Applied Mathematics

Statistics

Decision Maths

Pure Maths

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