Explanation Given Information: The provided function is f ( x ) = x x 2 − 1 . Formula used: The difference of the square formula. a 2 − b 2 = ( a − b ) ( a + b ) Calculation: Consider the provided function, f ( x ) = x x 2 − 1 . Since, the provided function is a rational function. The condition when the function f ( x ) = x x 2 − 1 is not defined is, x 2 − 1 = 0 x = ± 1 So, the domain of the provided function is all real number except the points ± 1 . Therefore the interval on which the function f ( x ) = x x 2 − 1 is continuous are ( − ∞ , − 1 ) , ( − 1 , 1 ) and ( 1 , ∞ ) . Take the limit of the provided function at x tends to − 1 . lim x → − 1 f ( x ) = lim x → − 1 ( ( − 1 ) ( − 1 ) 2 − 1 ) = ( − 1 1 − 1 ) = − 1 0 The limit of the function gives an undefined value at the point x = − 1 , Take the limit of the provided function at x tends to 1 . lim x → 1 f ( x ) = lim x → 1 ( 1 ( 1 ) 2 − 1 ) = ( 1 1 − 1 ) = 1 0 The limit of the function gives an undefined value at the points x = 1 . The limit of the provided function does not exist at points x = ± 1 . Now, choose some values for x and compute the value for f ( x ) , in order to form the ordered pairs that will plot on the graph. The provided function can be written as, use the difference of square formula a 2 − b 2 = ( a − b ) ( a + b ) . f ( x ) = x x 2 − 1 = x ( x − 1 ) ( x + 1 ) So, put x = − 2 in the above function

CALCULUS APPLIED APPROACH >PRINT UGRADE<

10th Edition

ISBN: 9780357667231

Author: Larson

Publisher: CENGAGE L

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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 1.6, Problem 17E

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To calculate: The interval(s) on which the function f(x)=xx2−1 is continuous and estimate the conditions that are not satisfied, if the function f(x)=xx2−1 has any discontinuity.

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Chapter 1 Solutions

CALCULUS APPLIED APPROACH >PRINT UGRADE<

Ch. 1.1 - Plot the points (3,2),(4,2),(3,1),(0,2),and(1,2)....Ch. 1.1 - The numbers E (in thousands of people) of...Ch. 1.1 - Find the distance between the points (-2, 1) and...Ch. 1.1 - Checkpoint 4 Worked-out solution available at...Ch. 1.1 - Checkpoint 5 Worked-out solution available at...Ch. 1.1 - Checkpoint 5 Worked-out solution available at...Ch. 1.1 - Checkpoint 5 Worked-out solution available at...Ch. 1.1 - Find the vertices of the parallelogram in Example...Ch. 1.1 - In Exercises 1-6, simplify the expression. 5+(4)2 Ch. 1.1 - In Exercises 1-6, simplify the expression. 3+(1)2

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The interval(s) on which the function f ( x ) = x x 2 − 1 is continuous and estimate the conditions that are not satisfied, if the function f ( x ) = x x 2 − 1 has any discontinuity.

Solution Summary: The author calculates the interval(s) on which the function f(x)=x

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To calculate: The interval(s) on which the function f(x)=xx2−1 is continuous and estimate the conditions that are not satisfied, if the function f(x)=xx2−1 has any discontinuity.

Chapter 1 Solutions