Explanation Given information: The function f ( x ) = { a x − 4 x − 2 if x ≠ 2 b if x = 2 . Condition for continuity: A function f ( x ) is continuous at a point x = a if and only if 1). f ( a ) is defined. 2). lim x → a f ( x ) exists. 3). lim x → a f ( x ) = f ( a ) Calculation: The rational function a x − 4 x − 2 is undefined at x = 2 . So, the domain will be { x ∈ R | x ≠ 2 } . The function f ( x ) is defined for all values of x. The only doubt point is x = 2 because f ( x ) is continuous for all x. Check continuity at x = 2 . A function f ( x ) is continuous at a point x = 2 if and only if Satisfy the following conditions: 1). f ( 2 ) = b So, the function f ( 2 ) is defined. 2). When x approaches 2 from left hand side or right-hand side that means x should be x ≠ 2 . So, the function will be f ( x ) = a x − 4 x − 2

7th Edition

ISBN: 9781524916817

Author: SMITH KARL J, STRAUSS MONTY J, TODA MAGDALENA DANIELE

Publisher: Kendall Hunt Publishing

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Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as:

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Chapter 2.3, Problem 39PS

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To find the constant a and b so that the given function will be continuous for all x .

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Chapter 2.3, Problem 38PS

Chapter 2.3, Problem 40PS

Chapter 2 Solutions

Calculus

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To find the constant a and b so that the given function will be continuous for all x .

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To find the constant a and b so that the given function will be continuous for all x .

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Chapter 2 Solutions