Explanation Given information: The function a ( t ) = t 2 if t > 0 and 0 otherwise. Formula used: If a function f is continuous at a point say a then lim x → a f ( x ) is the value of the function at that point that is lim x → a f ( x ) = f ( a ) , plug the limit in the function to evaluate the value. Calculation: Consider the provided function, a ( t ) = t 2 if t > 0 and 0 otherwise. The value of the expression lim t → 0 a ( t ) is evaluated when t is substitute as 0 in the expression a ( t ) = t 2 , lim t → 0 a ( t ) = lim t → 0 ( t 2 ) = 0 The value of the function a ( t ) = t 2 , 0.1 below the limiting argument that is t = − 0.1 , a ( − 0.1 ) = 0 The value of the function a ( t ) = t 2 , 0

Modeling the Dynamics of Life: Calculus and Probability for Life Scientists

3rd Edition

ISBN: 9780840064189

Author: Frederick R. Adler

Publisher: Cengage Learning

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Concept explainers

Limits of Multivariable Functions

Multivariable calculus is an extension of single variable calculus. It involves several variables instead of just one. Assume there is an open set containing points (x0, y0), let f be a function defined in that open interval except for the points (x0, y0…

Question

Chapter 2.3, Problem 20E

To determine

To calculate: The value of the expression limt→0a(t) , where a(t)=t2 if t>0 and 0 otherwise. Also estimate the value of function 0.1 and 0.01 above and below the limiting argument.

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Chapter 2.3, Problem 19E

Chapter 2.3, Problem 21E

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Chapter 2 Solutions

Modeling the Dynamics of Life: Calculus and Probability for Life Scientists

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. 2.2 - Prob. 1E Ch. 2.2 - Prob. 2E Ch. 2.2 - Prob. 3E Ch. 2.2 - Prob. 4E Ch. 2.2 - Prob. 5E Ch. 2.2 - Prob. 6E Ch. 2.2 - Prob. 7E Ch. 2.2 - Prob. 8E Ch. 2.2 - Prob. 9E Ch. 2.2 - Prob. 10E Ch. 2.2 - Prob. 11E Ch. 2.2 - Prob. 12E Ch. 2.2 - Prob. 13E Ch. 2.2 - Prob. 14E Ch. 2.2 - 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