Explanation A limit of a function at a point a is defined as the value that the function approaches as its argument approaches point a . The notation of limit is as follows: lim x → a ( f ( x ) ) = L , which is read as “limit of f ( x ) as x approaches a is L ” One-Sided Limits: A one-sided limit is a limit that only takes into account the values of a function that approaches a value from only one side i.e. either above or below. The right-side limit of a function f as it approaches a is give as lim x → a + ( f ( x ) ) = L The left-side limit of a function f as it approaches a is give as lim x → a − ( f ( x ) ) = L If right-side limit and left-side limit of a function are the same, then a two-sided limit exists for the function. Given: Given that A = lim x → a ( f ( x ) ) , B = lim x → a ( g ( x ) ) and L = lim x → a ( f ( x ) g ( x ) ) And L = 1 Formula Used: 1. lim x → a ( f ( x ) g ( x ) ) = lim x → a f ( x ) × lim x → a g ( x ) 2

3rd Edition

ISBN: 9781464125263

Author: Jon Rogawski, Colin Adams

Publisher: W.H. Freeman & Co

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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, Problem 65CRE

To determine

The fact that if L = 1, then A = B. Given that A = limx→a(f(x)), B = limx→a(g(x)) and L = limx→a(f(x)g(x))

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Chapter 2, Problem 64CRE

Chapter 2, Problem 66CRE

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Chapter 2 Solutions

Calculus - Standalone book

Ch. 2.1 - Prob. 1PQ Ch. 2.1 - Prob. 2PQ Ch. 2.1 - Prob. 3PQ Ch. 2.1 - Prob. 4PQ Ch. 2.1 - Prob. 5PQ Ch. 2.1 - Prob. 1E Ch. 2.1 - Prob. 2E Ch. 2.1 - Prob. 3E Ch. 2.1 - Prob. 4E Ch. 2.1 - Prob. 5E

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The fact that if L = 1 , then A = B . Given that A = lim x → a ( f ( x ) ) , B = lim x → a ( g ( x ) ) and L = lim x → a ( f ( x ) g ( x ) )

Solution Summary: The author explains that if L= 1 is a function's limit, then it is the value that the function approaches as its argument approaches point a .

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The fact that if L = 1, then A = B. Given that A = limx→a(f(x)), B = limx→a(g(x)) and L = limx→a(f(x)g(x))

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Chapter 2 Solutions