The graph of the functions.

Question

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Answer 1

Question

Chapter 2, Problem 33SP

(a)

To determine

To sketch:The graph of the functions.

(a)

Expert Solution

Explanation of Solution

Given information:

Consider the equation with increasing temperature, Vi(t)={T if T≤50100 if50<T≤100} and with decreasing temperature, Vd(t)={T if T≤20100 if20<T≤100}

Calculation:

The graph of the voltage with increasing temperature Vi(t)={T if T≤50100 if50<T≤100} is shown below as,

Modeling the Dynamics of Life: Calculus and Probability for Life Scientists, Chapter 2, Problem 33SP , additional homework tip 1

The graph of the voltage with decreasing temperature Vd(t)={T if T≤20100 if20<T≤100} is shown below as,

Modeling the Dynamics of Life: Calculus and Probability for Life Scientists, Chapter 2, Problem 33SP , additional homework tip 2

(b)

To determine

To find:The left and right hand limits of Vi,Vd as T approaches 50.

(b)

Expert Solution

Answer to Problem 33SP

The left hand limits are Vi=50,Vd=100

The right hand limits are Vi=100,Vd=100

Explanation of Solution

Given information:

Consider the equation with increasing temperature, Vi(t)={T if T≤50100 if50<T≤100} and with decreasing temperature, Vd(t)={T if T≤20100 if20<T≤100}

Calculation:

The left hand limit of increasing temperature Vi(t)={T if T≤50100 if50<T≤100} and Vd(t)={T if T≤20100 if20<T≤100} as T approaches 50 is calculated as,

limT→50−Vi(T)=limT→50T=50limT→50−Vd(T)=limT→50T=100

The right hand limit of decreasing temperature Vi(t)={T if T≤50100 if50<T≤100} and Vd(t)={T if T≤20100 if20<T≤100} as T approaches 50 is calculated as,

limT→50+Vi(T)=100limT→50+Vd(T)=100

Hence, the left hand limits are Vi=50,Vd=100 and the right hand limits are Vi=100,Vd=100

(c)

To determine

To find:The left and right hand limits of Vi,Vd as T approaches 20.

(c)

Expert Solution

Answer to Problem 33SP

The left hand limits are Vi=20,Vd=20

The right hand limits are Vi=20,Vd=100

Explanation of Solution

Given information:

Consider the equation with increasing temperature, Vi(t)={T if T≤50100 if50<T≤100} and with decreasing temperature, Vd(t)={T if T≤20100 if20<T≤100}

Calculation:

The left hand limit of increasing temperature Vi(t)={T if T≤50100 if50<T≤100} and Vd(t)={T if T≤20100 if20<T≤100} as T approaches 20 is calculated as,

limT→20−Vi(T)=limT→20T=20limT→20−Vd(T)=limT→20T=20

The right hand limit of decreasing temperature Vi(t)={T if T≤50100 if50<T≤100} and Vd(t)={T if T≤20100 if20<T≤100} as T approaches 20 is calculated as,

limT→20+Vi(T)=20limT→20+Vd(T)=100

The left hand limits are Vi=20,Vd=20

The right hand limits are Vi=20,Vd=100

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Answer 2

Question

Chapter 2, Problem 33SP

(a)

To determine

To sketch:The graph of the functions.

(a)

Expert Solution

Explanation of Solution

Given information:

Consider the equation with increasing temperature, Vi(t)={T if T≤50100 if50<T≤100} and with decreasing temperature, Vd(t)={T if T≤20100 if20<T≤100}

Calculation:

The graph of the voltage with increasing temperature Vi(t)={T if T≤50100 if50<T≤100} is shown below as,

Modeling the Dynamics of Life: Calculus and Probability for Life Scientists, Chapter 2, Problem 33SP , additional homework tip 1

The graph of the voltage with decreasing temperature Vd(t)={T if T≤20100 if20<T≤100} is shown below as,

Modeling the Dynamics of Life: Calculus and Probability for Life Scientists, Chapter 2, Problem 33SP , additional homework tip 2

(b)

To determine

To find:The left and right hand limits of Vi,Vd as T approaches 50.

(b)

Expert Solution

Answer to Problem 33SP

The left hand limits are Vi=50,Vd=100

The right hand limits are Vi=100,Vd=100

Explanation of Solution

Given information:

Consider the equation with increasing temperature, Vi(t)={T if T≤50100 if50<T≤100} and with decreasing temperature, Vd(t)={T if T≤20100 if20<T≤100}

Calculation:

The left hand limit of increasing temperature Vi(t)={T if T≤50100 if50<T≤100} and Vd(t)={T if T≤20100 if20<T≤100} as T approaches 50 is calculated as,

limT→50−Vi(T)=limT→50T=50limT→50−Vd(T)=limT→50T=100

The right hand limit of decreasing temperature Vi(t)={T if T≤50100 if50<T≤100} and Vd(t)={T if T≤20100 if20<T≤100} as T approaches 50 is calculated as,

limT→50+Vi(T)=100limT→50+Vd(T)=100

Hence, the left hand limits are Vi=50,Vd=100 and the right hand limits are Vi=100,Vd=100

(c)

To determine

To find:The left and right hand limits of Vi,Vd as T approaches 20.

(c)

Expert Solution

Answer to Problem 33SP

The left hand limits are Vi=20,Vd=20

The right hand limits are Vi=20,Vd=100

Explanation of Solution

Given information:

Consider the equation with increasing temperature, Vi(t)={T if T≤50100 if50<T≤100} and with decreasing temperature, Vd(t)={T if T≤20100 if20<T≤100}

Calculation:

The left hand limit of increasing temperature Vi(t)={T if T≤50100 if50<T≤100} and Vd(t)={T if T≤20100 if20<T≤100} as T approaches 20 is calculated as,

limT→20−Vi(T)=limT→20T=20limT→20−Vd(T)=limT→20T=20

The right hand limit of decreasing temperature Vi(t)={T if T≤50100 if50<T≤100} and Vd(t)={T if T≤20100 if20<T≤100} as T approaches 20 is calculated as,

limT→20+Vi(T)=20limT→20+Vd(T)=100

The left hand limits are Vi=20,Vd=20

The right hand limits are Vi=20,Vd=100

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Answer 3

Question

Chapter 2, Problem 33SP

(a)

To determine

To sketch:The graph of the functions.

(a)

Expert Solution

Explanation of Solution

Given information:

Consider the equation with increasing temperature, Vi(t)={T if T≤50100 if50<T≤100} and with decreasing temperature, Vd(t)={T if T≤20100 if20<T≤100}

Calculation:

The graph of the voltage with increasing temperature Vi(t)={T if T≤50100 if50<T≤100} is shown below as,

Modeling the Dynamics of Life: Calculus and Probability for Life Scientists, Chapter 2, Problem 33SP , additional homework tip 1

The graph of the voltage with decreasing temperature Vd(t)={T if T≤20100 if20<T≤100} is shown below as,

Modeling the Dynamics of Life: Calculus and Probability for Life Scientists, Chapter 2, Problem 33SP , additional homework tip 2

(b)

To determine

To find:The left and right hand limits of Vi,Vd as T approaches 50.

(b)

Expert Solution

Answer to Problem 33SP

The left hand limits are Vi=50,Vd=100

The right hand limits are Vi=100,Vd=100

Explanation of Solution

Given information:

Consider the equation with increasing temperature, Vi(t)={T if T≤50100 if50<T≤100} and with decreasing temperature, Vd(t)={T if T≤20100 if20<T≤100}

Calculation:

The left hand limit of increasing temperature Vi(t)={T if T≤50100 if50<T≤100} and Vd(t)={T if T≤20100 if20<T≤100} as T approaches 50 is calculated as,

limT→50−Vi(T)=limT→50T=50limT→50−Vd(T)=limT→50T=100

The right hand limit of decreasing temperature Vi(t)={T if T≤50100 if50<T≤100} and Vd(t)={T if T≤20100 if20<T≤100} as T approaches 50 is calculated as,

limT→50+Vi(T)=100limT→50+Vd(T)=100

Hence, the left hand limits are Vi=50,Vd=100 and the right hand limits are Vi=100,Vd=100

(c)

To determine

To find:The left and right hand limits of Vi,Vd as T approaches 20.

(c)

Expert Solution

Answer to Problem 33SP

The left hand limits are Vi=20,Vd=20

The right hand limits are Vi=20,Vd=100

Explanation of Solution

Given information:

Consider the equation with increasing temperature, Vi(t)={T if T≤50100 if50<T≤100} and with decreasing temperature, Vd(t)={T if T≤20100 if20<T≤100}

Calculation:

The left hand limit of increasing temperature Vi(t)={T if T≤50100 if50<T≤100} and Vd(t)={T if T≤20100 if20<T≤100} as T approaches 20 is calculated as,

limT→20−Vi(T)=limT→20T=20limT→20−Vd(T)=limT→20T=20

The right hand limit of decreasing temperature Vi(t)={T if T≤50100 if50<T≤100} and Vd(t)={T if T≤20100 if20<T≤100} as T approaches 20 is calculated as,

limT→20+Vi(T)=20limT→20+Vd(T)=100

The left hand limits are Vi=20,Vd=20

The right hand limits are Vi=20,Vd=100

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Answer 4

Question

Chapter 2, Problem 33SP

(a)

To determine

To sketch:The graph of the functions.

(a)

Expert Solution

Explanation of Solution

Given information:

Consider the equation with increasing temperature, Vi(t)={T if T≤50100 if50<T≤100} and with decreasing temperature, Vd(t)={T if T≤20100 if20<T≤100}

Calculation:

The graph of the voltage with increasing temperature Vi(t)={T if T≤50100 if50<T≤100} is shown below as,

Modeling the Dynamics of Life: Calculus and Probability for Life Scientists, Chapter 2, Problem 33SP , additional homework tip 1

The graph of the voltage with decreasing temperature Vd(t)={T if T≤20100 if20<T≤100} is shown below as,

Modeling the Dynamics of Life: Calculus and Probability for Life Scientists, Chapter 2, Problem 33SP , additional homework tip 2

(b)

To determine

To find:The left and right hand limits of Vi,Vd as T approaches 50.

(b)

Expert Solution

Answer to Problem 33SP

The left hand limits are Vi=50,Vd=100

The right hand limits are Vi=100,Vd=100

Explanation of Solution

Given information:

Consider the equation with increasing temperature, Vi(t)={T if T≤50100 if50<T≤100} and with decreasing temperature, Vd(t)={T if T≤20100 if20<T≤100}

Calculation:

The left hand limit of increasing temperature Vi(t)={T if T≤50100 if50<T≤100} and Vd(t)={T if T≤20100 if20<T≤100} as T approaches 50 is calculated as,

limT→50−Vi(T)=limT→50T=50limT→50−Vd(T)=limT→50T=100

The right hand limit of decreasing temperature Vi(t)={T if T≤50100 if50<T≤100} and Vd(t)={T if T≤20100 if20<T≤100} as T approaches 50 is calculated as,

limT→50+Vi(T)=100limT→50+Vd(T)=100

Hence, the left hand limits are Vi=50,Vd=100 and the right hand limits are Vi=100,Vd=100

(c)

To determine

To find:The left and right hand limits of Vi,Vd as T approaches 20.

(c)

Expert Solution

Answer to Problem 33SP

The left hand limits are Vi=20,Vd=20

The right hand limits are Vi=20,Vd=100

Explanation of Solution

Given information:

Consider the equation with increasing temperature, Vi(t)={T if T≤50100 if50<T≤100} and with decreasing temperature, Vd(t)={T if T≤20100 if20<T≤100}

Calculation:

The left hand limit of increasing temperature Vi(t)={T if T≤50100 if50<T≤100} and Vd(t)={T if T≤20100 if20<T≤100} as T approaches 20 is calculated as,

limT→20−Vi(T)=limT→20T=20limT→20−Vd(T)=limT→20T=20

The right hand limit of decreasing temperature Vi(t)={T if T≤50100 if50<T≤100} and Vd(t)={T if T≤20100 if20<T≤100} as T approaches 20 is calculated as,

limT→20+Vi(T)=20limT→20+Vd(T)=100

The left hand limits are Vi=20,Vd=20

The right hand limits are Vi=20,Vd=100

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Answer 5

Chapter 2, Problem 33SP

(a)

To determine

To sketch:The graph of the functions.

(a)

Expert Solution

Explanation of Solution

Given information:

Consider the equation with increasing temperature, Vi(t)={T if T≤50100 if50<T≤100} and with decreasing temperature, Vd(t)={T if T≤20100 if20<T≤100}

Calculation:

The graph of the voltage with increasing temperature Vi(t)={T if T≤50100 if50<T≤100} is shown below as,

Modeling the Dynamics of Life: Calculus and Probability for Life Scientists, Chapter 2, Problem 33SP , additional homework tip 1

The graph of the voltage with decreasing temperature Vd(t)={T if T≤20100 if20<T≤100} is shown below as,

Modeling the Dynamics of Life: Calculus and Probability for Life Scientists, Chapter 2, Problem 33SP , additional homework tip 2

(b)

To determine

To find:The left and right hand limits of Vi,Vd as T approaches 50.

(b)

Expert Solution

Answer to Problem 33SP

The left hand limits are Vi=50,Vd=100

The right hand limits are Vi=100,Vd=100

Explanation of Solution

Given information:

Consider the equation with increasing temperature, Vi(t)={T if T≤50100 if50<T≤100} and with decreasing temperature, Vd(t)={T if T≤20100 if20<T≤100}

Calculation:

The left hand limit of increasing temperature Vi(t)={T if T≤50100 if50<T≤100} and Vd(t)={T if T≤20100 if20<T≤100} as T approaches 50 is calculated as,

limT→50−Vi(T)=limT→50T=50limT→50−Vd(T)=limT→50T=100

The right hand limit of decreasing temperature Vi(t)={T if T≤50100 if50<T≤100} and Vd(t)={T if T≤20100 if20<T≤100} as T approaches 50 is calculated as,

limT→50+Vi(T)=100limT→50+Vd(T)=100

Hence, the left hand limits are Vi=50,Vd=100 and the right hand limits are Vi=100,Vd=100

(c)

To determine

To find:The left and right hand limits of Vi,Vd as T approaches 20.

(c)

Expert Solution

Answer to Problem 33SP

The left hand limits are Vi=20,Vd=20

The right hand limits are Vi=20,Vd=100

Explanation of Solution

Given information:

Consider the equation with increasing temperature, Vi(t)={T if T≤50100 if50<T≤100} and with decreasing temperature, Vd(t)={T if T≤20100 if20<T≤100}

Calculation:

The left hand limit of increasing temperature Vi(t)={T if T≤50100 if50<T≤100} and Vd(t)={T if T≤20100 if20<T≤100} as T approaches 20 is calculated as,

limT→20−Vi(T)=limT→20T=20limT→20−Vd(T)=limT→20T=20

The right hand limit of decreasing temperature Vi(t)={T if T≤50100 if50<T≤100} and Vd(t)={T if T≤20100 if20<T≤100} as T approaches 20 is calculated as,

limT→20+Vi(T)=20limT→20+Vd(T)=100

The left hand limits are Vi=20,Vd=20

The right hand limits are Vi=20,Vd=100

Answer 6

Chapter 2, Problem 33SP

(a)

To determine

To sketch:The graph of the functions.

(a)

Expert Solution

Explanation of Solution

Given information:

Consider the equation with increasing temperature, Vi(t)={T if T≤50100 if50<T≤100} and with decreasing temperature, Vd(t)={T if T≤20100 if20<T≤100}

Calculation:

The graph of the voltage with increasing temperature Vi(t)={T if T≤50100 if50<T≤100} is shown below as,

Modeling the Dynamics of Life: Calculus and Probability for Life Scientists, Chapter 2, Problem 33SP , additional homework tip 1

The graph of the voltage with decreasing temperature Vd(t)={T if T≤20100 if20<T≤100} is shown below as,

Modeling the Dynamics of Life: Calculus and Probability for Life Scientists, Chapter 2, Problem 33SP , additional homework tip 2

Answer 7

Chapter 2, Problem 33SP

(a)

To determine

To sketch:The graph of the functions.

Answer 8

(a)

Expert Solution

Explanation of Solution

Given information:

Consider the equation with increasing temperature, Vi(t)={T if T≤50100 if50<T≤100} and with decreasing temperature, Vd(t)={T if T≤20100 if20<T≤100}

Calculation:

The graph of the voltage with increasing temperature Vi(t)={T if T≤50100 if50<T≤100} is shown below as,

Modeling the Dynamics of Life: Calculus and Probability for Life Scientists, Chapter 2, Problem 33SP , additional homework tip 1

The graph of the voltage with decreasing temperature Vd(t)={T if T≤20100 if20<T≤100} is shown below as,

Modeling the Dynamics of Life: Calculus and Probability for Life Scientists, Chapter 2, Problem 33SP , additional homework tip 2

Answer 9

(a)

Expert Solution

Answer 10

(a)

Expert Solution

Answer 11

Expert Solution

Answer 12

(b)

To determine

To find:The left and right hand limits of Vi,Vd as T approaches 50.

(b)

Expert Solution

Answer to Problem 33SP

The left hand limits are Vi=50,Vd=100

The right hand limits are Vi=100,Vd=100

Explanation of Solution

Given information:

Consider the equation with increasing temperature, Vi(t)={T if T≤50100 if50<T≤100} and with decreasing temperature, Vd(t)={T if T≤20100 if20<T≤100}

Calculation:

The left hand limit of increasing temperature Vi(t)={T if T≤50100 if50<T≤100} and Vd(t)={T if T≤20100 if20<T≤100} as T approaches 50 is calculated as,

limT→50−Vi(T)=limT→50T=50limT→50−Vd(T)=limT→50T=100

The right hand limit of decreasing temperature Vi(t)={T if T≤50100 if50<T≤100} and Vd(t)={T if T≤20100 if20<T≤100} as T approaches 50 is calculated as,

limT→50+Vi(T)=100limT→50+Vd(T)=100

Hence, the left hand limits are Vi=50,Vd=100 and the right hand limits are Vi=100,Vd=100

Answer 13

(b)

To determine

To find:The left and right hand limits of Vi,Vd as T approaches 50.

Answer 14

(b)

Expert Solution

Answer to Problem 33SP

The left hand limits are Vi=50,Vd=100

The right hand limits are Vi=100,Vd=100

Answer 15

(b)

Expert Solution

Answer 16

(b)

Expert Solution

Answer 17

Expert Solution

Answer 18

Explanation of Solution

Given information:

Consider the equation with increasing temperature, Vi(t)={T if T≤50100 if50<T≤100} and with decreasing temperature, Vd(t)={T if T≤20100 if20<T≤100}

Calculation:

The left hand limit of increasing temperature Vi(t)={T if T≤50100 if50<T≤100} and Vd(t)={T if T≤20100 if20<T≤100} as T approaches 50 is calculated as,

limT→50−Vi(T)=limT→50T=50limT→50−Vd(T)=limT→50T=100

The right hand limit of decreasing temperature Vi(t)={T if T≤50100 if50<T≤100} and Vd(t)={T if T≤20100 if20<T≤100} as T approaches 50 is calculated as,

limT→50+Vi(T)=100limT→50+Vd(T)=100

Hence, the left hand limits are Vi=50,Vd=100 and the right hand limits are Vi=100,Vd=100

Answer 19

(c)

To determine

To find:The left and right hand limits of Vi,Vd as T approaches 20.

(c)

Expert Solution

Answer to Problem 33SP

The left hand limits are Vi=20,Vd=20

The right hand limits are Vi=20,Vd=100

Explanation of Solution

Given information:

Consider the equation with increasing temperature, Vi(t)={T if T≤50100 if50<T≤100} and with decreasing temperature, Vd(t)={T if T≤20100 if20<T≤100}

Calculation:

The left hand limit of increasing temperature Vi(t)={T if T≤50100 if50<T≤100} and Vd(t)={T if T≤20100 if20<T≤100} as T approaches 20 is calculated as,

limT→20−Vi(T)=limT→20T=20limT→20−Vd(T)=limT→20T=20

The right hand limit of decreasing temperature Vi(t)={T if T≤50100 if50<T≤100} and Vd(t)={T if T≤20100 if20<T≤100} as T approaches 20 is calculated as,

limT→20+Vi(T)=20limT→20+Vd(T)=100

The left hand limits are Vi=20,Vd=20

The right hand limits are Vi=20,Vd=100

Answer 20

(c)

To determine

To find:The left and right hand limits of Vi,Vd as T approaches 20.

Answer 21

(c)

Expert Solution

Answer to Problem 33SP

The left hand limits are Vi=20,Vd=20

The right hand limits are Vi=20,Vd=100

Answer 22

(c)

Expert Solution

Answer 23

(c)

Expert Solution

Answer 24

Expert Solution

Answer 25

Explanation of Solution

Given information:

Consider the equation with increasing temperature, Vi(t)={T if T≤50100 if50<T≤100} and with decreasing temperature, Vd(t)={T if T≤20100 if20<T≤100}

Calculation:

The left hand limit of increasing temperature Vi(t)={T if T≤50100 if50<T≤100} and Vd(t)={T if T≤20100 if20<T≤100} as T approaches 20 is calculated as,

limT→20−Vi(T)=limT→20T=20limT→20−Vd(T)=limT→20T=20

The right hand limit of decreasing temperature Vi(t)={T if T≤50100 if50<T≤100} and Vd(t)={T if T≤20100 if20<T≤100} as T approaches 20 is calculated as,