Explanation Given: lim x → ∞ 2 x x − 100 Concept Used: 1. L'Hopital's Rule: If f and g are differentiable functions and g ( x ) is nonzero, and if lim x → c f ( x ) g ( x ) is of the indeterminate form, then lim x → c f ( x ) g ( x ) = lim x → c f ′ ( x ) g ′ ( x ) 2. Exponential growth function a k x always dominates power function x r ; that is, lim x → ∞ a k x > lim x → ∞ x r Calculation: To evaluate the limit lim x → ∞ 2 x x − 100 First write it as lim x → ∞ 2 x x − 100 = lim x → ∞ 2 x x 100 Using the concept that exponential growth function dominates power function, thus lim x → ∞ 2 x > lim x → ∞ x 100 Which implies that the denominator of the function is very large then the numerator

14th Edition

ISBN: 9781464140051

Author: TAALMAN, Laura, Kohn, Peter

Publisher: W. H. Freeman

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Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topic…

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Chapter 3.6, Problem 79S

To determine

To find the limit (if it exists)

limx→∞2xx−100

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Chapter 3.6, Problem 78S

Chapter 3.6, Problem 80S

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