Chapter 1: Q. 13 (page 148)

Describe in terms of large and small numbers why it makes intuitive sense that limits of the form (a) $\frac{1}{0^{+}}$ (b) $\frac{\infty}{0^{+}}$ (c) $\frac{\infty}{1}$ must be infinite.

Short Answer

Expert verified

(a) The limit $\frac{1}{0^{+}}$ is infinity and is very large.

(b) The limit $\frac{\infty}{0^{+}}$ is infinity and is very large.

Step by step solution

Step 1. Given Information

The given limits are $\frac{\infty}{0^{+}}, \frac{\infty}{0^{+}}$ and $\frac{\infty}{1}$

Part (a) Step 1. Explanation of Limit of the form 10+

$\lim_{x \to 0^{+}} \frac{1}{x} = \infty$

The limit is approaching from right and any number divide by zero is infinity.

A number when divided by zero gives infinity.

Part (b) Step 1. Explanation of limit ∞0+

$\lim_{x \to 0^{+}} \frac{1}{x} = \infty$

The limit is approaching from right and any number divide by zero is infinity.

Part (c) Step 1. Explanation of limit ∞1

The limit $\frac{\infty}{1}$ is $\infty$ because the numerator has $\infty$ and any number when divided by 1, result itself.

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Describe in terms of large and small numbers why it makes intuitive sense that limits of the form (a) $\frac{1}{0^{+}}$ (b) $\frac{\infty}{0^{+}}$ (c) $\frac{\infty}{1}$ must be infinite.

Short Answer

Step by step solution

Step 1. Given Information

Part (a) Step 1. Explanation of Limit of the form 10+

Part (b) Step 1. Explanation of limit ∞0+

Part (c) Step 1. Explanation of limit ∞1

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Describe in terms of large and small numbers why it makes intuitive sense that limits of the form (a) 10+(b) ∞0+(c) ∞1must be infinite.

Short Answer

Step by step solution

Step 1. Given Information

Part (a) Step 1. Explanation of Limit of the form 10+

Part (b) Step 1. Explanation of limit ∞0+

Part (c) Step 1. Explanation of limit ∞1

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

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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) $\frac{1}{0^{+}}$ (b) $\frac{\infty}{0^{+}}$ (c) $\frac{\infty}{1}$ must be infinite.