Explanation Given information : The statement “If f is continuous at 5 and f ( 5 ) = 2 and f ( 4 ) = 3 , then lim x → 2 f ( 4 x 2 − 11 ) = 2 .” Consider the provided statement “If f is continuous at 5 and f ( 5 ) = 2 and f ( 4 ) = 3 , then lim x → 2 f ( 4 x 2 − 11 ) = 2 .” Recall that if a function say p is continuous at an arbitrary point r and lim x → s q ( x ) = r , this implies that lim x → s p ( q ( x ) ) = f ( r ) . Take the expression lim x → 2 f ( 4 x 2 − 11 ) = 2 , the term 4 x 2 − 11 is a polynomial function which is continuous at every point on real number line. Therefore, the function and limit can be moved through each other. Now, lim x → 2 f ( 4 x 2 − 11 ) = f ( lim x → 2 ( 4 x 2 − 11 ) ) Evaluate the limit of the function at x = 2

15th Edition

ISBN: 9781133109631

Author: Stewart, JAMES, Day, Troy

Publisher: Cengage Learning,

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Chapter 2, Problem 15TFQ

To determine

To find: Whether the statement “If f is continuous at 5 and f(5)=2 and f(4)=3 , then limx→2f(4x2−11)=2 .” is true or false.

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Chapter 2, Problem 14TFQ

Chapter 2, Problem 16TFQ

Chapter 2 Solutions

Biocalculus

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

Ch. 2.1 - Prob. 11E Ch. 2.1 - Prob. 12E Ch. 2.1 - Prob. 13E Ch. 2.1 - Prob. 14E Ch. 2.1 - Prob. 15E Ch. 2.1 - Prob. 16E Ch. 2.1 - Prob. 17E Ch. 2.1 - Prob. 18E Ch. 2.1 - Prob. 19E Ch. 2.1 - Prob. 20E Ch. 2.1 - Prob. 21E Ch. 2.1 - Prob. 22E Ch. 2.1 - Prob. 23E Ch. 2.1 - Prob. 24E Ch. 2.1 - Prob. 25E Ch. 2.1 - Prob. 26E Ch. 2.1 - Prob. 27E Ch. 2.1 - Prob. 28E Ch. 2.1 - Prob. 29E Ch. 2.1 - Prob. 30E Ch. 2.1 - Prob. 31E Ch. 2.1 - Prob. 32E Ch. 2.1 - Prob. 33E Ch. 2.1 - Prob. 34E Ch. 2.1 - Prob. 35E Ch. 2.1 - Prob. 36E Ch. 2.1 - Prob. 37E Ch. 2.1 - Prob. 38E Ch. 2.1 - Prob. 39E Ch. 2.1 - Prob. 40E Ch. 2.1 - Prob. 41E Ch. 2.1 - Prob. 42E Ch. 2.1 - Prob. 43E Ch. 2.1 - Prob. 44E Ch. 2.1 - Prob. 45E Ch. 2.1 - Prob. 46E Ch. 2.1 - Prob. 47E Ch. 2.1 - Prob. 48E Ch. 2.1 - Prob. 49E Ch. 2.1 - Prob. 50E Ch. 2.1 - Prob. 51E Ch. 2.1 - Prob. 52E Ch. 2.1 - Prob. 53E Ch. 2.1 - Prob. 54E Ch. 2.1 - Prob. 55E Ch. 2.1 - Prob. 56E Ch. 2.1 - Prob. 57E Ch. 2.1 - Prob. 58E Ch. 2.1 - Prob. 59E Ch. 2.1 - Prob. 60E Ch. 2.1 - 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Prob. 9CS

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Limits and Continuity; Author: The Organic Chemistry Tutor;https://www.youtube.com/watch?v=9brk313DjV8;License: Standard YouTube License, CC-BY

Whether the statement “If f is continuous at 5 and f ( 5 ) = 2 and f ( 4 ) = 3 , then lim x → 2 f ( 4 x 2 − 11 ) = 2 .” is true or false.

Solution Summary: The author explains whether the statement "If f is continuous at 5 and

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To find: Whether the statement “If f is continuous at 5 and f(5)=2 and f(4)=3 , then limx→2f(4x2−11)=2 .” is true or false.

Want to see the full answer?

Chapter 2 Solutions