Explanation Given information: Given function is f ( x ) = ⌈ x ⌉ − ⌊ x ⌋ n is the unique integer such that n − 1 < x ≤ n . Concept used: A function f ( x ) is continuous at x = a if lim x → a + f ( x ) = lim x → a − f ( x ) = lim x → a f ( x ) Calculation: ⌈ x ⌉ is least integer function. ⌊ x ⌋ is greatest integer function. Graph of the function f ( x ) = ⌈ x ⌉ − ⌊ x ⌋ is shown below. For every integern, lim x → n + f ( x ) = lim x → n + ⌈ x ⌉ − ⌊ x ⌋ = n − ( n + 1 ) = n − n − 1 = − 1 This shows that f ( x ) = ⌈ x ⌉ − ⌊ x ⌋ is right − continuous at x = n

4th Edition

ISBN: 9781319050740

Author: Jon Rogawski, Colin Adams, Robert Franzosa

Publisher: W. H. Freeman

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Question

Chapter 2.4, Problem 56E

To determine

To find the type of discontinuity for the function f(x)=⌈x⌉−⌊x⌋

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Chapter 2.4, Problem 55E

Chapter 2.4, Problem 57E

Chapter 2 Solutions

Calculus: Early Transcendentals

Ch. 2.1 - Prob. 1PQ Ch. 2.1 - Prob. 2PQ Ch. 2.1 - Prob. 3PQ Ch. 2.1 - Prob. 4PQ 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 Ch. 2.1 - Prob. 6E

Ch. 2.1 - Prob. 7E Ch. 2.1 - Prob. 8E Ch. 2.1 - Prob. 9E Ch. 2.1 - Prob. 10E Ch. 2.1 - Prob. 11E Ch. 2.1 - Prob. 12E Ch. 2.1 - Prob. 13E Ch. 2.1 - Prob. 14E Ch. 2.1 - Prob. 15E Ch. 2.1 - Prob. 16E Ch. 2.1 - Prob. 17E Ch. 2.1 - Prob. 18E Ch. 2.1 - Prob. 19E Ch. 2.1 - Prob. 20E Ch. 2.1 - Prob. 21E Ch. 2.1 - Prob. 22E Ch. 2.1 - Prob. 23E Ch. 2.1 - Prob. 24E Ch. 2.1 - Prob. 25E Ch. 2.1 - Prob. 26E Ch. 2.1 - Prob. 27E Ch. 2.1 - Prob. 28E Ch. 2.1 - Prob. 29E Ch. 2.1 - Prob. 30E Ch. 2.1 - Prob. 31E Ch. 2.1 - Prob. 32E Ch. 2.1 - Prob. 33E Ch. 2.2 - Prob. 1PQ Ch. 2.2 - Prob. 2PQ Ch. 2.2 - Prob. 3PQ Ch. 2.2 - Prob. 4PQ Ch. 2.2 - Prob. 5PQ Ch. 2.2 - Prob. 6PQ Ch. 2.2 - Prob. 7PQ Ch. 2.2 - Prob. 1E Ch. 2.2 - Prob. 2E Ch. 2.2 - Prob. 3E Ch. 2.2 - Prob. 4E Ch. 2.2 - Prob. 5E Ch. 2.2 - Prob. 6E Ch. 2.2 - Prob. 7E Ch. 2.2 - Prob. 8E Ch. 2.2 - Prob. 9E Ch. 2.2 - Prob. 10E Ch. 2.2 - Prob. 11E Ch. 2.2 - Prob. 12E Ch. 2.2 - Prob. 13E Ch. 2.2 - Prob. 14E Ch. 2.2 - Prob. 15E Ch. 2.2 - Prob. 16E Ch. 2.2 - Prob. 17E Ch. 2.2 - 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To find the type of discontinuity for the function f ( x ) = ⌈ x ⌉ − ⌊ x ⌋

Solution Summary: The author explains the type of discontinuity for the function f(x)=lceil x

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To find the type of discontinuity for the function f(x)=⌈x⌉−⌊x⌋

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Chapter 2 Solutions