Chapter 1: Q. 11 (page 148)

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

Short Answer

Expert verified

All the three limits equal to zero.

Step by step solution

Step 1. Given Information

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

Step 2. Explanation

$\frac{1}{\infty}$ is zero because any number divided by infinity approaches to zero.

$\frac{0}{\infty}$ is zero because any number divided by infinity approaches to zero.

$\frac{0}{1}$ is zero.

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

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Explanation

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Describe in terms of large and small numbers why it makes intuitive sense that limits of the form a1∞b0∞(c)01must equal 0.

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Explanation

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