Explanation Given: A function: g ( x ) = x 2 − 1 x 2 + x − 2 Calculation: We know that a rational function is discontinuous, when the denominator is equal to zero. Let us find zeros of denominator as shown below: x 2 + x − 2 = 0 x 2 + 2 x − x − 2 = 0 x ( x + 2 ) − 1 ( x + 2 ) = 0 ( x + 2 ) ( x − 1 ) = 0 ( x + 2 ) = 0 , ( x − 1 ) = 0 x = − 2 , x = 1 We can factor out numerator and denominator as shown below:

7th Edition

ISBN: 9781524916817

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

Publisher: Kendall Hunt Publishing

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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, Problem 27PE

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Whether the given function is continuous on the interval [−5,5] .

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Chapter 2, Problem 26PE

Chapter 2, Problem 28PE

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Chapter 2 Solutions

Calculus

Ch. 2.1 - Prob. 1PS Ch. 2.1 - Prob. 2PS Ch. 2.1 - Prob. 3PS Ch. 2.1 - Prob. 4PS Ch. 2.1 - Prob. 5PS Ch. 2.1 - Prob. 6PS Ch. 2.1 - Prob. 7PS Ch. 2.1 - Prob. 8PS Ch. 2.1 - Prob. 9PS Ch. 2.1 - Prob. 10PS

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Whether the given function is continuous on the interval [ − 5 , 5 ] .

Solution Summary: The author explains that the given function is not continuous on the interval [-5,5].

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Whether the given function is continuous on the interval [−5,5] .

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Chapter 2 Solutions