Explanation Procedure used: L’ Hospital’s rule: 1: Check whether the lim x → a f ( x ) g ( x ) is an indeterminate form 0 0 or ± ∞ ± ∞ . 2: If so obtain the derivative of f ( x ) and g ( x ) , separately. 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 ) . 4 If it does not exist repeat the step 2 and step 3. Calculation: Step 1: Obtain the value of lim x → 0 + x e 1 x . lim x → 0 + x e 1 x = lim x → 0 + ( x e 1 x ) = ( ( 0 ) e 1 0 ) = undefined ( ∵ e 1 0 is undefined ) Thus, apply L’Hospital’s rule. Step 2: Rewrite the lim x → 0 + x e 1 x as lim x → 0 + ( e 1 x ) ( 1 x ) . Where f ( x ) = ( e 1 x ) and g ( x ) = 1 x Obtain the derivative of f ( x )

Calculus with Applications Books a la Carte Edition

11th Edition

ISBN: 9780133864564

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

Publisher: Pearson Education

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Chapter 12.7, Problem 34E

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The value of limx→0+xe1x by applying the L’Hospital’s rule.

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Chapter 12.7, Problem 33E

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The value of lim x → 0 + x e 1 x by applying the L’Hospital’s rule.

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

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The value of limx→0+xe1x by applying the L’Hospital’s rule.

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