Chapter 1: Q.8 (page 148)

Determine which of the given forms are indeterminate. For each form that is not indeterminate, describe the behavior of a limit of that form.
$\infty \cdot \infty 0 \cdot \infty 5 \cdot \infty 5 \cdot 0 0.0$

Short Answer

Expert verified

The indeterminate forms are $0 \cdot \infty a n d 5 \cdot \infty$

Step by step solution

Step 1. Given Information

The given limits are $\infty \cdot \infty 0 \cdot \infty 5 \cdot \infty 5 \cdot 0 0.0$

Step 2. identifying Indeterminate forms

$\infty \cdot \infty$ is Non-Indeterminate Forms for Limits because the result is also infinity.

$0 \cdot \infty$ is -Indeterminate Forms for Limits because Infinity is an undefined number (having no finite value), multiplying Infinity by Zero results in an undefined value.

$5 \cdot \infty$ is -Indeterminate Forms for Limits Infinity is not considered a number, so infinity times three is technically undefined or no answer, because infinity is not necessarily a number.

$5 \cdot 0$ is Non-Indeterminate Forms for Limits because any number multiplied by zero is zero.

$0 \cdot 0$ multiplying by zero always gives zero,

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Determine which of the given forms are indeterminate. For each form that is not indeterminate, describe the behavior of a limit of that form.
$\infty \cdot \infty 0 \cdot \infty 5 \cdot \infty 5 \cdot 0 0.0$

Short Answer

Step by step solution

Step 1. Given Information

Step 2. identifying Indeterminate forms

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Determine which of the given forms are indeterminate. For each form that is not indeterminate, describe the behavior of a limit of that form.∞·∞0·∞5·∞5·00.0

Short Answer

Step by step solution

Step 1. Given Information

Step 2. identifying Indeterminate forms

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Applied Mathematics

Geometry

Discrete Mathematics

Pure Maths

Logic and Functions

Study anywhere. Anytime. Across all devices.

Determine which of the given forms are indeterminate. For each form that is not indeterminate, describe the behavior of a limit of that form.
$\infty \cdot \infty 0 \cdot \infty 5 \cdot \infty 5 \cdot 0 0.0$