Chapter 3: Q. 1 (page 309)

Indeterminate forms: Determine which of the given forms are indeterminate. For each form that is not indeterminate, describe the behavior of a limit of that form.
$\infty . \infty \frac{\infty}{\infty} 0^{0} \infty^{\infty} \frac{0}{0} 1^{\infty} \infty - \infty \frac{0}{\infty} 0^{\infty} \infty . 0 \frac{\infty}{0} \infty^{0}$

Short Answer

Expert verified

The indeterminate form and the other forms of limit are:

\infty . \infty = \infty \frac{\infty}{\infty} i s a n i n d e t e r m i n a t e f o r m . 0^{0} i s a n i n d e t e r m i n a t e f o r m . \infty^{\infty} = \infty \frac{0}{0} i s a n i n d e t e r m i n a t e f o r m . 1^{\infty} i s a n i n d e t e r m i n a t e f o r m . \infty - \infty i s a n i n d e t e r m i n a t e f o r m . \frac{0}{\infty} = 0 0^{\infty} = 0 \infty . 0 i s a n i n d e t e r m i n a t e f o r m . \frac{\infty}{0} = \infty \infty^{0} i s a n i n d e t e r m i n a t e f o r m .

Step by step solution

Step 1. Given Information.

Some forms:

$\infty . \infty \frac{\infty}{\infty} 0^{0} \infty^{\infty} \frac{0}{0} 1^{\infty} \infty - \infty \frac{0}{\infty} 0^{\infty} \infty . 0 \frac{\infty}{0} \infty^{0}$

Step 2. An indeterminate form.

An indeterminate form is the value that we are unable to value.

$\infty . \infty = \infty \frac{\infty}{\infty} i s a n i n d e t e r m i n a t e f o r m . 0^{0} i s a n i n d e t e r m i n a t e f o r m . \infty^{\infty} = \infty \frac{0}{0} i s a n i n d e t e r m i n a t e f o r m . 1^{\infty} i s a n i n d e t e r m i n a t e f o r m . \infty - \infty i s a n i n d e t e r m i n a t e f o r m . \frac{0}{\infty} = 0 0^{\infty} = 0 \infty . 0 i s a n i n d e t e r m i n a t e f o r m . \frac{\infty}{0} = \infty \infty^{0} i s a n i n d e t e r m i n a t e f o r m .$

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Short Answer

Step by step solution

Step 1. Given Information.

Step 2. An indeterminate form.

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Indeterminate forms: 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∞∞001∞∞-∞0∞0∞∞.0∞0∞0

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. An indeterminate form.

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Most popular questions from this chapter

Recommended explanations on Math Textbooks

Pure Maths

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