Explanation Theorem used: Limits of the linear functions . Let a, b and m be real numbers. For linear functions f ( x ) = m x + b , lim x → a f ( x ) = f ( a ) = m a + b . Sum law: Assume lim x → a f ( x ) and lim x → a g ( x ) exist, then lim x → a ( f ( x ) + g ( x ) ) = lim x → a f ( x ) + lim x → a g ( x ) . Calculation: Evaluate the limit as follows. lim x → a x 3 − a 3 x − a = lim x → a ( x − a ) ( x 2 + a x + a 2 )

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ISBN: 9781323178522

Author: Briggs

Publisher: PEARSON

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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 2.3, Problem 52E

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To evaluate: The limit of the function limx→ax3−a3x−a .

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Chapter 2.3, Problem 51E

Chapter 2.3, Problem 53E

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The limit of the function lim x → a x 3 − a 3 x − a .

Solution Summary: The author evaluates the limit of the linear function 3a2. Let a, b, and m be real numbers.

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To evaluate: The limit of the function limx→ax3−a3x−a .

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Chapter 2 Solutions