Explanation Given: The function f ( x ) = { x + 1 , if x < 1 3 x − 1 , if 1 ≤ x < 2 x + 2 , if x ≥ 2 Concept used: The left continuity and right continuity of a function f at a point x = c are , equal lim x → a − f ( x ) = f ( a ) lim x → a + f ( x ) = f ( a ) Calculation: The function f ( x ) = { x + 1 , if x < 1 3 x − 1 , if 1 ≤ x < 2 x + 2 , if x ≥ 2 ............. ( 1 ) Putting x = 1 in equation (1) f ( 1 ) = 3 x − 1 f ( 1 ) = 3 × 1 − 1 f ( 1 ) = 2 The left continuity and right continuity of a function f at a point x = c are , equal lim x → a − f ( x ) = f ( a ) lim x → a + f ( x ) = f ( a ) Left continuity lim x → a ȡ

5th Edition

ISBN: 9781429241861

Author: Laura Taalman, Peter Kohn

Publisher: W. H. Freeman

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Question

Chapter 1.4, Problem 43S

To determine

The function f(x)={x+1, if x<13x−1 , if 1≤x<2x+2, if x≥2 is continuous or not at the value of x .

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Chapter 1.4, Problem 42S

Chapter 1.4, Problem 44S

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Chapter 1 Solutions

Calculus

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The function f ( x ) = { x + 1 , if x < 1 3 x − 1 , if 1 ≤ x < 2 x + 2 , if x ≥ 2 is continuous or not at the value of x .

Solution Summary: The author calculates the left continuity and right continuity of a function f at x=c.

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The function f(x)={x+1, if x<13x−1 , if 1≤x<2x+2, if x≥2 is continuous or not at the value of x .

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The function f ( x ) = { x + 1 , if x &lt; 1 3 x − 1 , if 1 ≤ x &lt; 2 x + 2 , if x ≥ 2 is continuous or not at the value of x .

Solution Summary: The author calculates the left continuity and right continuity of a function f at x=c.

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The function f(x)={x+1, if x<13x−1 , if 1≤x<2x+2, if x≥2 is continuous or not at the value of x .

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Chapter 1 Solutions

The function f ( x ) = { x + 1 , if x < 1 3 x − 1 , if 1 ≤ x < 2 x + 2 , if x ≥ 2 is continuous or not at the value of x .