Chapter 1: Q. 9 (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.
$\frac{0}{0}, \frac{0}{\infty}, \frac{\infty}{0}, \frac{1}{0}, \frac{0}{1}, \frac{\infty}{1}, \frac{1}{\infty}, \frac{\infty}{\infty}$

Short Answer

Expert verified

The indeterminate forms are $\frac{0}{0}, \frac{\infty}{0}, \frac{\infty}{\infty}$

Step by step solution

Step 1. Given Information

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

Step 2. Identifying Indeterminate forms

$\frac{0}{0}$ is Indeterminate forms of limit because is not a real number and we cannot actually

divide the number 0 by the number 0.

$\frac{0}{\infty}$ is Non-Indeterminate forms of limit the behavior of both the numerator and the denominator causes the limit to approach 0.

$\frac{\infty}{0}$ is one of the indeterminate forms having a large range of different values.

$\frac{1}{0}$ is not defined.

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

$\frac{\infty}{1}$ is infinity because any number divide by 1, is itself the number. It is Non-Indeterminate forms of limit.

$\frac{1}{\infty}$ is zero because $\infty$ is a very large number and divided by $\infty$ approaches to zero.

$\frac{\infty}{\infty}$ is indeterminate form because $\infty$ is again a undefined.

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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.
$\frac{0}{0}, \frac{0}{\infty}, \frac{\infty}{0}, \frac{1}{0}, \frac{0}{1}, \frac{\infty}{1}, \frac{1}{\infty}, \frac{\infty}{\infty}$

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.00,0∞,∞0,10,01,∞1,1∞,∞∞

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

Statistics

Decision Maths

Geometry

Applied Mathematics

Probability and Statistics

Theoretical and Mathematical Physics

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.
$\frac{0}{0}, \frac{0}{\infty}, \frac{\infty}{0}, \frac{1}{0}, \frac{0}{1}, \frac{\infty}{1}, \frac{1}{\infty}, \frac{\infty}{\infty}$