a. Explanation Given: lim x → ∞ 3 x 1 − 4 x Concept Used: lim x → ∞ ( α ) x = 0 ; if − 1 < α <1 L'Hopital's Rule: If f and g are differentiable functions and g ( x ) is nonzero, and if lim x → c f ( x ) g ( x ) is of the indeterminate form, then lim x → c f ( x ) g ( x ) = lim x → c f ′ ( x ) g ′ ( x ) Calculation: To calculate the limit lim x → ∞ 3 x 1 − 4 x First see that the putting the limit directly in this function gives lim x → ∞ 3 x 1 − 4 x = 3 ∞ 1 − 4 ∞ = − ∞ ∞ As, lim x → ∞ 3 x 1 − b. To determine To calculate the limit lim x → ∞ 3 x 1 − 4 x Without using L’Hopital’s Rule.

5th Edition

ISBN: 9781429241861

Author: Laura Taalman, Peter Kohn

Publisher: W. H. Freeman

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Sequence and Series

A sequence is defined as a collection of things. Series is defined to sum the things one by one in the sequence. It was invented by German mathematician Carl Friedrich Gauss.

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Chapter 3.6, Problem 18S

To determine

To calculate the limit

limx→∞3x1−4x

Using L'Hopital's Rule.

To determine

To calculate the limit

limx→∞3x1−4x

Without using L’Hopital’s Rule.

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Chapter 3.6, Problem 17S

Chapter 3.6, Problem 19S

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To calculate the limit lim x → ∞ 3 x 1 − 4 x Using L'Hopital's Rule.

Solution Summary: The author explains how to calculate the limit using L'Hopital's Rule. If f and g are differentiable functions, and undersetxto cmathrm

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To calculate the limit

limx→∞3x1−4x

Using L'Hopital's Rule.

To calculate the limit

limx→∞3x1−4x

Without using L’Hopital’s Rule.

Want to see the full answer?

Chapter 3 Solutions

To calculate the limit lim x → ∞ 3 x 1 − 4 x Using L'Hopital's Rule.

Solution Summary: The author explains how to calculate the limit using L'Hopital's Rule. If f and g are differentiable functions, and undersetxto cmathrm

Concept explainers

Videos

To calculate the limit limx→∞3x1−4x Using L'Hopital's Rule.

To calculate the limit limx→∞3x1−4x Without using L’Hopital’s Rule.

Want to see the full answer?

Chapter 3 Solutions

To calculate the limit

limx→∞3x1−4x

Using L'Hopital's Rule.

To calculate the limit

limx→∞3x1−4x

Without using L’Hopital’s Rule.