Chapter 1: Q. 40 (page 153)

Indeterminate forms: Identify which of the limit forms listed here are indeterminate. For each form that is not indeterminate, describe the behavior of a limit of that form.
$\frac{\infty}{1} .$

Short Answer

Expert verified

Given limit form is not indeterminate and it will be always $\infty$ .

Step by step solution

Step 1. Given Information.

$G i v e n a l i m i t f o r m : \frac{\infty}{1} .$

Step 2. Indeterminate forms available.

$W e h a v e f o l l o w i n g 7 i n d e t e r m i n a t e f o r m s a v a i l a b l e w i t h u s : \infty^{0}, \infty - \infty, \frac{0}{0}, \frac{\infty}{\infty}, 0^{0}, 0 \times \infty, 1^{\infty} .$

Step 3. Determining the value of the limit form given.

Since, it is clear that it is not an indeterminate form.

Now, it's value will be $\infty$ always because whatever be the numerator but if denominator is 1 then it doesn't affect the value in the numerator. If denominator is 1 then it can be ignored and it's value will be equal to numerator as well.

That's why, $\frac{\infty}{1} = \infty .$

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Indeterminate forms: Identify which of the limit forms listed here are indeterminate. For each form that is not indeterminate, describe the behavior of a limit of that form.
$\frac{\infty}{1} .$

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. Indeterminate forms available.

Step 3. Determining the value of the limit form given.

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Indeterminate forms: Identify which of the limit forms listed here are indeterminate. For each form that is not indeterminate, describe the behavior of a limit of that form.∞1.

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. Indeterminate forms available.

Step 3. Determining the value of the limit form given.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

Logic and Functions

Discrete Mathematics

Statistics

Mechanics Maths

Pure Maths

Study anywhere. Anytime. Across all devices.

Indeterminate forms: Identify which of the limit forms listed here are indeterminate. For each form that is not indeterminate, describe the behavior of a limit of that form.
$\frac{\infty}{1} .$