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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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

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The value of the expression lim t → 0 a ( t ) , where a ( t ) = t 2 if t > 0 and 0 otherwise. Also estimate the value of function 0.1 and 0.01 above and below the limiting argument.

Solution Summary: The author calculates the value of the expression undersettto 0mathrmlima(t

Concept explainers

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 Solutions

The value of the expression lim t → 0 a ( t ) , where a ( t ) = t 2 if t &gt; 0 and 0 otherwise. Also estimate the value of function 0.1 and 0.01 above and below the limiting argument.

Solution Summary: The author calculates the value of the expression undersettto 0mathrmlima(t

Concept explainers

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.

Want to see the full answer?

Chapter 2 Solutions

The value of the expression lim t → 0 a ( t ) , where a ( t ) = t 2 if t > 0 and 0 otherwise. Also estimate the value of function 0.1 and 0.01 above and below the limiting argument.