Explanation Given information: The quantity of a drug in the bloodstream t hours after a tablet is swallowed is given, in mg, by q ( t ) = 20 ( e − t − e − 2 t ) Formula used: Calculation: The quantity of a drug in the bloodstream t hours is given by q ( t ) = 20 ( e − t − e − 2 t ) (Given)</ To determine (b) To calculate: The time at which maximum quantity of drug in the bloodstream and the maximum value. To determine (c) To calculate: The quantity in long run.

Applied Calculus, 6e WileyPLUS + Loose-leaf

6th Edition

ISBN: 9781119408901

Author: Deborah Hughes-Hallett, Andrew M. Gleason, Patti Frazer Lock, Daniel E. Flath

Publisher: Wiley (WileyPLUS Products)

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Question

Chapter 4.3, Problem 57P

To determine

(a)

To calculate:

The amount of drug in the bloodstream at time t=0.

To determine

(b)

To calculate:

The time at which maximum quantity of drug in the bloodstream and the maximum value.

To determine

(c)

To calculate:

The quantity in long run.

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Chapter 4.3, Problem 56P

Chapter 4.3, Problem 58P

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I circled the correct answer, could you show me how to do it using divergence and polar coordinates

The correct answer is D Could you explain and show the steps please

Taylor Series Approximation Example- H.W More terms used implies better approximation f(x) 4 f(x) Zero order f(x + 1) = f(x;) First order f(x; + 1) = f(x;) + f'(x;)h 1.0 Second order 0.5 True f(x + 1) = f(x) + f'(x)h + ƒ"(x;) h2 2! f(x+1) 0 x; = 0 x+1 = 1 x h f(x)=0.1x4-0.15x³- 0.5x2 -0.25x + 1.2 51 Taylor Series Approximation H.w: Smaller step size implies smaller error Errors f(x) + f(x,) Zero order f(x,+ 1) = f(x) First order 1.0 0.5 Reduced step size Second order True f(x + 1) = f(x) + f'(x)h f(x; + 1) = f(x) + f'(x)h + "(xi) h2 f(x,+1) O x₁ = 0 x+1=1 Using Taylor Series Expansion estimate f(1.35) with x0 =0.75 with 5 iterations (or & s= 5%) for f(x)=0.1x 0.15x³-0.5x²- 0.25x + 1.2 52

Chapter 4 Solutions

Applied Calculus, 6e WileyPLUS + Loose-leaf

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(a) To calculate: The amount of drug in the bloodstream at time t = 0.

Solution Summary: The author calculates the amount of drug in the bloodstream at time t=0.

Concept explainers

Videos

(a)

To calculate:

The amount of drug in the bloodstream at time t=0.

(b)

To calculate:

The time at which maximum quantity of drug in the bloodstream and the maximum value.

(c)

To calculate:

The quantity in long run.

Want to see the full answer?

Chapter 4 Solutions

(a) To calculate: The amount of drug in the bloodstream at time t = 0.

Solution Summary: The author calculates the amount of drug in the bloodstream at time t=0.

Concept explainers

Videos

(a) To calculate: The amount of drug in the bloodstream at time t=0.

(b) To calculate: The time at which maximum quantity of drug in the bloodstream and the maximum value.

(c) To calculate: The quantity in long run.

Want to see the full answer?

Chapter 4 Solutions

(a)

To calculate:

The amount of drug in the bloodstream at time t=0.

(b)

To calculate:

The time at which maximum quantity of drug in the bloodstream and the maximum value.

(c)

To calculate:

The quantity in long run.