Chapter 1: Q. 14 (page 148)

Describe in terms of large and small numbers why it makes intuitive sense that limits of the form $(a) \infty + \infty (b) \infty \cdot \infty (c) \infty^{1}$ must be infinite.

Short Answer

Expert verified

(a) The limit $\infty + \infty$ is infinity and is a large number.

(b) The limit $\infty \cdot \infty$ is infinity and is a large number.

Step by step solution

Step 1. Given Information

The given limits are $\infty + \infty, \infty \cdot \infty$ and $\infty^{1}$

Part (a) Step 1. The limit ∞+∞

The limit of the form $\infty + \infty$ is non-indeterminate form and it gives a very large number.

Part(b) Step 1. The limit ∞·∞

The infinity multiplied by infinity is infinity which is a large number.

Part (c) Step 1. The limit ∞1

$\infty^{1} = \infty$ because any number raised power 1 is itself the number.

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Describe in terms of large and small numbers why it makes intuitive sense that limits of the form $(a) \infty + \infty (b) \infty \cdot \infty (c) \infty^{1}$ must be infinite.

Short Answer

Step by step solution

Step 1. Given Information

Part (a) Step 1. The limit ∞+∞

Part(b) Step 1. The limit ∞·∞

Part (c) Step 1. The limit ∞1

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Describe in terms of large and small numbers why it makes intuitive sense that limits of the forma∞+∞(b)∞·∞(c)∞1must be infinite.

Short Answer

Step by step solution

Step 1. Given Information

Part (a) Step 1. The limit ∞+∞

Part(b) Step 1. The limit ∞·∞

Part (c) Step 1. The limit ∞1

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Logic and Functions

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Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

Describe in terms of large and small numbers why it makes intuitive sense that limits of the form $(a) \infty + \infty (b) \infty \cdot \infty (c) \infty^{1}$ must be infinite.