Explanation Given: lim x → c f ( x ) = L 1 ; lim x → c f ( x ) = L 2 . Here we have to prove that the L 1 = L 2 where L 1 = lim x → c f ( x ) ; L 2 = lim x → c f ( x ) . In other words we have to prove that a function converges to at most one limiting value. That means the limit of a function is unique if it exists. Calculation: Description: Step 1 : To prove this uniqueness property, we have to assign a function f : A → R and an accumulation point of A ⊂ R , which is denoted as c , where c ∈ R . L 1 = lim x → c f ( x ) L 2 = lim x → c f ( x ) Step 2 : Write the given limit definition of L 1 a n d L 2 , where L 1 , L 2 ∈ R . L 1 = lim x → c f ( x ) L 2 = lim x → c f ( x ) Step 3 : Define the existence of δ 1 , δ 2

3rd Edition

ISBN: 9781464125263

Author: Jon Rogawski, Colin Adams

Publisher: W.H. Freeman & Co

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Sequence and Series

A sequence is defined as a collection of things. Series is defined to sum the things one by one in the sequence. It was invented by German mathematician Carl Friedrich Gauss.

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Chapter 2.9, Problem 30E

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To prove that L1=L2 for given L1 and L2

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Chapter 2.9, Problem 29E

Chapter 2.9, Problem 31E

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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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To prove that L 1 = L 2 for given L 1 a n d L 2

Solution Summary: The author explains how to prove that a function converges to at least one limiting value.

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To prove that L1=L2 for given L1 and L2

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Chapter 2 Solutions