Explanation Given: The limit of a function, lim x → a f ( x ) = L , namely 0 < | x − a | < δ . Definition used-1: Assume that a function f exists for all x near with x > a . The limit of f ( x ) as x approaches a from the right of a is L and write lim x → a + f ( x ) = L , if for any ε > 0 there exists δ > 0 such that | f ( x ) − L | < ε whenever 0 < ( x − a ) < δ . Definition used-2: Assume that a function f exists for all x near with x < a . The limit of f ( x ) as x approaches a from the left of a is L and write lim x → a − f ( x ) = L , if for any ε > 0 there exists δ > 0 such that | f ( x ) − L | < ε whenever 0 < ( a − x ) < δ

Calculus, Single Variable: Early Transcendentals (3rd Edition)

3rd Edition

ISBN: 9780134766850

Author: William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz

Publisher: PEARSON

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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 2.7, Problem 52E

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To explain: The last inequality in the definition of limx→af(x)=L , namely 0<|x−a|<δ , replaced with 0<(a−x)<δ in the definition of limx→a−f(x)=L .

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Chapter 2.7, Problem 51E

Chapter 2.7, Problem 53E

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Use the graph to find the limit L (if it exists). If the limit does not exist, explain why. (If an answer does not exist, enter DNE.) g(x) = −2x x − 2 (a) lim x→2 g(x) L = The limit does not exist at x = 2 because the function does not approach f(2) as x approaches 2.The limit does not exist at x = 2 because the function is not continuous at any x value. The limit does not exist at x = 2 because f(2) ≠ 2.The limit does not exist at x = 2 because the function increases and decreases without bound as x approaches 2.The limit exists at x = 2. (b) lim x→0 g(x) L = The limit does not exist at x = 0 because the function does not approach f(0) as x approaches 0.The limit does not exist at x = 0 because the function is not continuous at any x value. The limit does not exist at x = 0 because f(0) ≠ 0.The limit does not exist at x = 0 because the function increases and decreases without bound as x approaches 0.The limit exists at x = 0.

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Chapter 2 Solutions

Calculus, Single Variable: Early Transcendentals (3rd Edition)

Ch. 2.1 - In Example 1, what is the average velocity between...Ch. 2.1 - Explain the difference between average velocity...Ch. 2.1 - Prob. 3QC Ch. 2.1 - Suppose s(t) is the position of an object moving...Ch. 2.1 - Suppose s(t) is the position of an object moving...Ch. 2.1 - Basic Skills 7. Average velocity The function s(t)...Ch. 2.1 - Average velocity The function s(t) represents the...Ch. 2.1 - Average velocity The table gives the position s(t)...Ch. 2.1 - Average velocity The graph gives the position s(t)...Ch. 2.1 - Instantaneous velocity The following table gives...

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The last inequality in the definition of lim x → a f ( x ) = L , namely 0 < | x − a | < δ , replaced with 0 < ( a − x ) < δ in the definition of lim x → a − f ( x ) = L .

Solution Summary: The author explains the last inequality in the definition of undersetxto amathrmlim

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To explain: The last inequality in the definition of limx→af(x)=L , namely 0<|x−a|<δ , replaced with 0<(a−x)<δ in the definition of limx→a−f(x)=L .

Want to see the full answer?

Chapter 2 Solutions

The last inequality in the definition of lim x → a f ( x ) = L , namely 0 &lt; | x − a | &lt; δ , replaced with 0 &lt; ( a − x ) &lt; δ in the definition of lim x → a − f ( x ) = L .

Solution Summary: The author explains the last inequality in the definition of undersetxto amathrmlim

Concept explainers

Videos

To explain: The last inequality in the definition of limx→af(x)=L , namely 0<|x−a|<δ , replaced with 0<(a−x)<δ in the definition of limx→a−f(x)=L .

Want to see the full answer?

Chapter 2 Solutions

The last inequality in the definition of lim x → a f ( x ) = L , namely 0 < | x − a | < δ , replaced with 0 < ( a − x ) < δ in the definition of lim x → a − f ( x ) = L .