Explanation Given information: A limit function is given as, lim x → 0 x 2 + sin x 2 x 2 + x 3 . Concept used: L'Hospital's Rule: If f and g are differentiable in an open interval containing a and f ( a ) = g ( a ) = 0 . Also, g ' ( x ) ≠ 0 (except possibly at a ). Then- lim x → a f ( x ) g ( x ) = lim x → a f ' ( x ) g ' ( x ) This rule is also applicable when f ( a ) = ± ∞ and g ( a ) = ± ∞ . Calculation: Given limit function is, lim x → 0 x 2 + sin x 2 x 2 + x 3 . Let us suppose, f ( x ) = x 2 + sin x 2 and g ( x ) = x 2 + x 3 . Here, a = 0 . So, f ( a ) = 0 2 + sin 0 2 = 0 and g ( a ) = 0 2 + 0 3 = 0 Therefore, limit converts into an indeterminate form of 0 0 . L'Hospital's Rule is applicable here

Student's Solution and Survival Manual for Calculus

7th Edition

ISBN: 9781524934040

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

Publisher: Kendall Hunt Publishing

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Chapter 4.5, Problem 16PS

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To calculate: The value of given limit.

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Chapter 4.5, Problem 15PS

Chapter 4.5, Problem 17PS

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Chapter 4 Solutions

Student's Solution and Survival Manual for Calculus

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The value of given limit.

Solution Summary: The author explains the L'Hospital's Rule for calculating the value of a given limit.

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Chapter 4 Solutions