Explanation Given information: The expression, lim x → 1 f ( x ) − 8 x − 1 = 10 . Formula used: The sum rule for limits, lim x → a ( m ( x ) + n ( x ) ) = lim x → a m ( x ) + lim x → a n ( x ) , where m ( x ) and n ( x ) are arbitrary functions. The product rule for limits, lim x → a ( m ( x ) ⋅ n ( x ) ) = lim x → a m ( x ) ⋅ lim x → a n ( x ) , where m ( x ) and n ( x ) are arbitrary functions. Calculation: Consider the expression, lim x → 1 f ( x ) − 8 x − 1 = 10 , Now, start with the expression, lim x → 1 ( f ( x ) ) . Add and subtract 8 within the brackets of limits, lim x → 1 ( f ( x ) ) = lim x → 1 ( f ( x ) − 8 + 8 ) Multiply and divide by ( x − 1 ) to the term f ( x ) − 8 , lim x → 1 ( f ( x ) ) = lim x → 1 ( f ( x ) − 8 + 8 ) = lim x → 1 ( [ f ( x ) − 8 ( x − 1 ) ] ( x − 1 ) + 8 ) Apply sum rule for limits, lim x → a ( m ( x ) + n ( x ) ) = lim x → a m ( x ) + lim x → a n ( x ) , where m ( x ) and n ( x ) are arbitrary functions

15th Edition

ISBN: 9781305420878

Author: Stewart

Publisher: CENGAGE L

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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 2.4, Problem 49E

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To calculate: The value of the expression limx→1f(x) if limx→1f(x)−8x−1=10 .

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Chapter 2.4, Problem 48E

Chapter 2.4, Problem 50E

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Chapter 2 Solutions

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The value of the expression lim x → 1 f ( x ) if lim x → 1 f ( x ) − 8 x − 1 = 10 .

Solution Summary: The author calculates the value of the expression undersetxto 1mathrmlimf(x-) if it is 8. The sum rule for limits is

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To calculate: The value of the expression limx→1f(x) if limx→1f(x)−8x−1=10 .

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Chapter 2 Solutions