Chapter 1: Q. 10 (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.
$0^{1}, 0^{0}, 0^{\infty}, 1^{\infty}, \infty^{1}, \infty^{0}, \infty^{\infty}$

Short Answer

Expert verified

The indeterminate forms are $0^{0}, 1^{\infty}, \infty^{0},$ and $\infty^{\infty}$

Step by step solution

Step 1. Given Information

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

Step 2. Identifying Indeterminate forms

$0^{1}$ is non-indeterminate forms and is equal to zero.

$0^{0}$ is indeterminate forms of limit because 0 to the power 0 is undefined!

$0^{\infty}$ is indeterminate forms .

$1^{\infty}$ is equal to one because one is multiplied by infinity gives 1.

$\infty^{1}$ is undefined. when infinity is multiplied by any number, answer will be zero.

$\infty^{0}$ is non-indeterminate forms and is equal to one.

$\infty^{\infty}$ is 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.
$0^{1}, 0^{0}, 0^{\infty}, 1^{\infty}, \infty^{1}, \infty^{0}, \infty^{\infty}$

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.01,00,0∞,1∞,∞1,∞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

Pure Maths

Discrete Mathematics

Statistics

Calculus

Mechanics Maths

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