Explanation Procedure used: L’ Hospital’s rule. Step 1: Check whether the lim x → a f ( x ) g ( x ) is an indeterminate form 0 0 or ± ∞ ± ∞ . Step 2: If so obtain the derivative of f ( x ) and g ( x ) , separately. Step 3: Compute the lim x → a f ′ ( x ) g ′ ( x ) , if this limit exist then lim x → a f ( x ) g ( x ) = lim x → a f ′ ( x ) g ′ ( x ) . Step 4 If it does not exist repeat the step 2 and step 3 . Calculation: From the given limit, f ( x ) = x 3 + x 2 − 11 x − 3 and g ( x ) = x 2 − 3 x . Step 1: Obtain the value of lim x → 3 x 3 + x 2 − 11 x − 3 x 2 − 3 x . lim x → 3 x 3 + x 2 − 11 x − 3 x 2 − 3 x = lim x → 3 ( 3 ) 3 + ( 3 ) 2 − 11 ( 3 ) − 3 ( 3 ) 2 − 3 ( 3 ) = 27 + 9 − 33 − 3 9 − 9 = 0 0 This is observed to be an indeterminate form

Calculus with Applications (11th Edition)

11th Edition

ISBN: 9780321979421

Author: Margaret L. Lial, Raymond N. Greenwell, Nathan P. Ritchey

Publisher: PEARSON

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Chapter 12.7, Problem 2E

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Calculus with Applications (11th Edition)

Ch. 12.1 - Find the first four terms of the sequence having...Ch. 12.1 - Prob. 2YT Ch. 12.1 - Prob. 3YT Ch. 12.1 - Prob. 4YT Ch. 12.1 - Prob. 5YT Ch. 12.1 - Prob. 1E Ch. 12.1 - Prob. 2E Ch. 12.1 - Prob. 3E Ch. 12.1 - List the first n terms of the geometric sequence...Ch. 12.1 - Prob. 5E

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The value of lim x → 3 x 3 + x 2 − 11 x − 3 x 2 − 3 x by applying the L’Hospital’s rule.

Solution Summary: The author calculates the value of undersetxto 3mathrmlim by applying the L’Hospital’s rule.

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The value of limx→3x3+x2−11x−3x2−3x by applying the L’Hospital’s rule.

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