(a) Explanation Given information: A model ρ e − q A = 1 − A , where A is the fraction of population infected, q is the measure of disease transferability and ρ is the initial susceptible population. Formula used: The Linear Approximation of a function f ( x ) at a point x = a is given by: f ( x ) ≈ f ( a ) + f ' ( a ) ( x − a ) Calculation: Since it is given ρ e − q A = 1 − A , it can be written as A = 1 − ρ e − q A Since A is a function of q , to find implicit differentiation with respect to q at q = 0 ; Differentiating implicitly with respect to q : A ' ( q ) = 0 − ρ e − q ( A ) q [ − A − q A ' ( q ) ] = ρ e − q A ( q ) [ A + q A ' ( q ) ] A ' ( q ) [ 1 − q ρ e (b) To determine To find: The second-order Taylor polynomial approximation for A ( q ) at q = 0 .

15th Edition

ISBN: 9781305177291

Author: James Stewart, Troy Day

Publisher: Cengage Learning

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Question

Chapter 3, Problem 92E

(a)

To determine

To find: The linear approximation of A as a function of q at q=0 using implicit differentiation.

(b)

To determine

To find: The second-order Taylor polynomial approximation for A(q) at q=0.

Expert Solution & Answer

Chapter 3 Solutions

Biocalculus: Calculus For Life Sciences

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The linear approximation of A as a function of q at q = 0 using implicit differentiation .

Solution Summary: The author explains the linear approximation of A as a function of qatq=0 using implicit differentiation.

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To find: The linear approximation of A as a function of q at q=0 using implicit differentiation.

To find: The second-order Taylor polynomial approximation for A(q) at q=0.

Chapter 3 Solutions