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. Given: The given limit is lim x → ∞ ( ln x ) e x . Calculation: Step 1: Obtain the value of lim x → ∞ ( ln x ) e x . lim x → ∞ ( ln x ) e x = ∞ ∞ It is observed to be an indeterminate form. Thus, apply L’Hospital’s rule. Step 2: It is noticed that f ( x ) = ( ln x ) and g ( x ) = e x To determine The value of the given limit by applying the L’Hospital’s rule.

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Chapter 12.7, Problem 6YT

To determine

The value of the given limit by applying the L’Hospital’s rule.

To determine

The value of the given limit by applying the L’Hospital’s rule.

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Chapter 12.7, Problem 5YT

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