Modeling the Dynamics of Life: Calculus and Probability for Life Scientists
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
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Chapter 2.3, Problem 19E
To determine

To calculate: The value of the expression limw→1r(w) , where r(w)=(1−w)−4 . Also estimate the value of function 0.1 and 0.01 above and below the limiting argument.

Expert Solution & Answer
Check Mark

Answer to Problem 19E

The value of the expression limw→1r(w)cannot be estimated, value of function 0.1 and 0.01 above and below the limiting argument are r(0.9)=10000 , r(1.1)=−10000 , r(0.99)=1.0×108 and r(1.01)=−1.0×108 .

Explanation of Solution

Given information:

The function r(w)=(1−w)−4 .

Formula used:

If a function f is continuous at a point say a then limx→af(x) is the value of the function at that point that is limx→af(x)=f(a) , plug the limit in the function to evaluate the value.

Calculation:

Consider the provided function, r(w)=(1−w)−4 .

The value of the expression limw→1r(w) is evaluated when w is substitute as 1 in the expression r(w)=(1−w)−4 ,

  limw→1r(w)=limw→1(1−w)−4=(1−1)−4=0−4

The limit cannot be estimated.

The value of the function r(w)=(1−w)−4 , 0.1 below the limiting argument that is w=0.9 ,

  r(0.9)=(1−0.9)−4=10000

The value of the function r(w)=(1−w)−4 , 0.1 above the limiting argument that is w=1.1 ,

  r(1.1)=(1−1.1)−4=−10000

The value of the function r(w)=(1−w)−4 , 0.01 below the limiting argument that is w=0.99 ,

  r(0.99)=(1−0.99)−4=1.0×108

The value of the function r(w)=(1−w)−4 , 0.01 above the limiting argument that is w=1.01 ,

  r(1.01)=(1−1.01)−4=−1.0×108

Thus, the value of the expression limw→1r(w) cannot be estimated, value of function 0.1 and 0.01 above and below the limiting argument are r(0.9)=10000 , r(1.1)=−10000 , r(0.99)=1.0×108 and r(1.01)=−1.0×108 .

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Chapter 2 Solutions

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

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