Explanation Given: A limit: lim x → 0 + ( 1 + x ) 4 x Concept used: L’Hospital’s rule states that if two functions f ( x ) and g ( x ) both approach 0 as x approaches c, then lim x → c f ( x ) g ( x ) = lim x → c f ' ( x ) g ' ( x ) . Calculation: First of all, we will write our given limit applying exponent rule a x = e ln ( a x ) as shown below: lim x → 0 + ( 1 + x ) 4 x = lim x → 0 + e ( ln ( 1 + x ) 4 x ) = lim x → 0 + e 4 x ⋅ ln ( 1 + x ) Now, we will use limit chain rule to solve our given limit as: g ( x ) = 4 x ⋅ ln ( 1 + x ) f ( u ) = e u Let us find limit of lim x → 0 + g ( x ) = lim x → 0 + ( 4 x ⋅ ln ( 1 + x ) ) = lim x → 0 + (

Calculus: Special Edition: Chapters 1-5 (w/ WebAssign)

6th Edition

ISBN: 9781524908102

Author: SMITH KARL J, STRAUSS MONTY J, TODA MAGDALENA DANIELE

Publisher: Kendall Hunt Publishing

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Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topic…

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Chapter 2, Problem 35SP

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The given limit limx→0+(1+x)4x .

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Chapter 2, Problem 34SP

Chapter 2, Problem 36SP

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Chapter 2 Solutions

Calculus: Special Edition: Chapters 1-5 (w/ WebAssign)

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The given limit lim x → 0 + ( 1 + x ) 4 x .

Solution Summary: The author evaluates the given limit using the exponent rule ax=emathrmln.

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To evaluate:

The given limit limx→0+(1+x)4x .

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Chapter 2 Solutions

The given limit lim x → 0 + ( 1 + x ) 4 x .

Solution Summary: The author evaluates the given limit using the exponent rule ax=emathrmln.

Concept explainers

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To evaluate: The given limit limx→0+(1+x)4x .

Want to see the full answer?

Chapter 2 Solutions

To evaluate:

The given limit limx→0+(1+x)4x .