Explanation Given information: The given limit statement is lim x → ∞ 2 x − 1 x = 2 . Concept used: For the limit statement lim x → ∞ f ( x ) = L , the delta-epsilon statement is For all ∈ > 0 , there exist N > 0 such that whenever x ≥ N guarantees f ( x ) ∈ ( L − ∈ , L + ∈ ) . Mathematically it can be written as for every x satisfying x ≥ N , every f ( x ) satisfies | f ( x ) − L | < ∈ . Calculation: Consider the given limit statement. lim x → ∞ 2 x − 1 x = 2 So, comparing the limit statement with lim x → ∞ f ( x ) = L , <

5th Edition

ISBN: 9781429241861

Author: Laura Taalman, Peter Kohn

Publisher: W. H. Freeman

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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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Question

Chapter 1.3, Problem 63P

To determine

To write: A δ−M , N−∈ or N−M proof for the given limit statement.

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Chapter 1.3, Problem 62P

Chapter 1.3, Problem 64P

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Chapter 1 Solutions

Calculus

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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ACP Ch. 1 - Prob. BCP Ch. 1 - Prob. CCP Ch. 1 - Prob. DCP

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A δ − M , N − ∈ or N − M proof for the given limit statement.

Solution Summary: The author explains how to write a delta -M, N-in or M proof for the given limit statement.

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To write: A δ−M , N−∈ or N−M proof for the given limit statement.

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Chapter 1 Solutions