Explanation Given information: The given limit statement is lim x → 3 1 x = 1 3 . assume δ ≤ 1 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 limit statement

14th Edition

ISBN: 9781464151088

Author: Associate Professor Laura Taalman, Peter Kohn

Publisher: W.H. Freeman & Company

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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 1.3, Problem 38S

To determine

To find: a positive value of δ in terms of ∈>0 such that the given limit statement satisfy the delta-epsilon statement.

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Chapter 1.3, Problem 37S

Chapter 1.3, Problem 39S

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a positive value of δ in terms of ∈ > 0 such that the given limit statement satisfy the delta-epsilon statement.

Solution Summary: The author explains that the given limit statement satisfy the delta-epsilon statement.

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To find: a positive value of δ in terms of ∈>0 such that the given limit statement satisfy the delta-epsilon statement.

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a positive value of δ in terms of ∈ &gt; 0 such that the given limit statement satisfy the delta-epsilon statement.

Solution Summary: The author explains that the given limit statement satisfy the delta-epsilon statement.

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To find: a positive value of δ in terms of ∈>0 such that the given limit statement satisfy the delta-epsilon statement.

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Chapter 1 Solutions

a positive value of δ in terms of ∈ > 0 such that the given limit statement satisfy the delta-epsilon statement.