10th Edition

Ron Larson + 1 other

ISBN: 9781285057095

Textbook Problem

Evaluating a Limit In Exercises 11–42, evaluate the limit, using L’Hôpital’s Rule if necessary.

lim x → ∞ x 2 + 4 x + 7 x − 6

To determine

To calculate: The value of limit limx→∞x2+4x+7x−6 by the use of L’Hospital’s Rule, if necessary.

The provided function is limx→∞x2+4x+7x−6.

Formula used:

L’Hospital’s Rule: If the limit of f(x)/g(x) when x approaches c from right produces indeterminate form 0/0, then limx→cf(x)g(x)=limx→cf′(x)g′(x)

Power rule: ddxxn=nxn−1

Calculation:

Consider the function x2+4x+7x−6.

Apply the limit x→∞ to the function x2+4x+7x−6.

Substitute ∞ for x,

limx→∞x2+4x+7x−6=∞2+4⋅∞+7∞−6=∞+∞+7∞=∞∞

As the direct substitution of limit produces indeterminate form ∞/∞, so L’Hospital’s Rule can be applied

Check out a sample textbook solution.

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Evaluating a Limit In Exercises 11–42, evaluate the limit, using L’Hôpital’s Rule if necessary.

lim x → ∞ x 2 + 4 x + 7 x − 6

Chapter 8 Solutions

Additional Math Solutions

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Calculus

Solutions

Calculus

Evaluating a Limit In Exercises 11–42, evaluate the limit, using L’Hôpital’s Rule if necessary. lim x → ∞ x 2 + 4 x + 7 x − 6

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Chapter 8 Solutions

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Calculus Calculus 10th Edition

Evaluating a Limit In Exercises 11–42, evaluate the limit, using L’Hôpital’s Rule if necessary.

lim x → ∞ x 2 + 4 x + 7 x − 6