Explanation Given information: The given inequality implication is if x ∈ ( 1 , 1 + δ ) then | x − 1 − 0 | < 0.5 . Concept used: For the limit statement lim x → c f ( x ) = L , the delta-epsilon statement is For all ∈ > 0 , there exist δ > 0 such that whenever x ∈ ( c − δ , c ) ∪ ( c , c + δ ) guarantees f ( x ) ∈ ( L − ∈ , L + ∈ ) . Mathematically it can be written as for every x satisfying 0 < | x − c | < δ , every f ( x ) satisfies | f ( x ) − L | < ∈ . Calculation: Consider the given interval. x ∈ ( 1 , 1 + δ ) The interval can be written in inequality form as shown: 1 < x < 1 + δ 1 − 1 < x − 1 < 1 + δ − 1 0 < x − 1 < δ 0 < | x − 1 | < δ

14th Edition

ISBN: 9781464151088

Author: Associate Professor Laura Taalman, Peter Kohn

Publisher: W.H. Freeman & Company

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Question

Chapter 1.3, Problem 25S

To determine

To find: the largest possible value of δ or smallest possible value of N that makes the given implication true. Verify the answer by graph.

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Chapter 1.3, Problem 24S

Chapter 1.3, Problem 26S

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The answer for number 1 is D Could you show me why

Chapter 1 Solutions

Calculus Combo

Ch. 1.1 - Prob. 1TB Ch. 1.1 - Prob. 2TB Ch. 1.1 - Prob. 0C Ch. 1.1 - Prob. 1C Ch. 1.1 - Prob. 2C Ch. 1.1 - Prob. 3C Ch. 1.1 - Prob. 4C Ch. 1.1 - Prob. 5C Ch. 1.1 - Prob. 6C Ch. 1.1 - Prob. 7C

Ch. 1.1 - Prob. 8C Ch. 1.1 - Prob. 9C Ch. 1.1 - Prob. 10C Ch. 1.1 - Prob. 11C Ch. 1.1 - Prob. 12C Ch. 1.1 - Prob. 13C Ch. 1.1 - Prob. 14C Ch. 1.1 - Prob. 15C Ch. 1.1 - Prob. 16C Ch. 1.1 - Prob. 17C Ch. 1.1 - Prob. 18C Ch. 1.1 - Prob. 19C Ch. 1.1 - Prob. 20C Ch. 1.1 - Prob. 21S Ch. 1.1 - Prob. 22S Ch. 1.1 - Prob. 23S Ch. 1.1 - Prob. 24S Ch. 1.1 - Prob. 25S Ch. 1.1 - Prob. 26S Ch. 1.1 - Prob. 27S Ch. 1.1 - Prob. 28S Ch. 1.1 - Prob. 29S Ch. 1.1 - Prob. 30S Ch. 1.1 - Prob. 31S Ch. 1.1 - Prob. 32S Ch. 1.1 - Prob. 33S Ch. 1.1 - Prob. 34S Ch. 1.1 - Prob. 35S Ch. 1.1 - Prob. 36S Ch. 1.1 - Prob. 37S Ch. 1.1 - Prob. 38S Ch. 1.1 - Prob. 39S Ch. 1.1 - Prob. 40S Ch. 1.1 - Prob. 41S Ch. 1.1 - Prob. 42S Ch. 1.1 - Prob. 43S Ch. 1.1 - Prob. 44S Ch. 1.1 - Prob. 45S Ch. 1.1 - Prob. 46S Ch. 1.1 - Prob. 47S Ch. 1.1 - Prob. 48S Ch. 1.1 - Prob. 49S Ch. 1.1 - Prob. 50S Ch. 1.1 - Prob. 51S Ch. 1.1 - Prob. 52S Ch. 1.1 - Prob. 53S Ch. 1.1 - Prob. 54S Ch. 1.1 - Prob. 55S Ch. 1.1 - Prob. 56S Ch. 1.1 - Prob. 57S Ch. 1.1 - 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the largest possible value of δ or smallest possible value of N that makes the given implication true. Verify the answer by graph.

Solution Summary: The author explains that the largest possible value of delta is 0.25.

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To find: the largest possible value of δ or smallest possible value of N that makes the given implication true. Verify the answer by graph.

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Chapter 1 Solutions