Numerical Analysis
Numerical Analysis
10th Edition
ISBN: 9781305730663
Author: Richard L. Burden; J. Douglas Faires; Annette M. Burden
Publisher: Cengage Learning US
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Chapter 2.3, Problem 28ES

A drug administered to a patient produces a concentration in the bloodstream given by c(t) = Atet/3 milligrams per milliliter, t hours after A units have been injected. The maximum safe concentration is 1 mg/mL.

  1. a. What amount should be injected to reach this maximum safe concentration, and when does this maximum occur?
  2. b. An additional amount of this drug is to be administered to the patient after the concentration falls to 0.25 mg/mL. Determine, to the nearest minute, when this second injection should be given.
  3. c. Assume that the concentration from consecutive injections is additive and that 75% of the amount originally injected is administered in the second injection. When is it time for the third injection?
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Chapter 2 Solutions

Numerical Analysis

Ch. 2.1 - Let f(x) = (x + 2)(x + 1)x(x 1)3(x 2). To which...Ch. 2.1 - Find an approximation to 253 correct to within 104...Ch. 2.1 - Find an approximation to 3 correct to within 104...Ch. 2.1 - A trough of length L has a cross section in the...Ch. 2.1 - Use Theorem 2.1 to find a bound for the number of...Ch. 2.1 - Prob. 18ESCh. 2.1 - Prob. 19ESCh. 2.1 - Let f(x) = (x 1)10, p = 1, and pn = 1 + 1/n. Show...Ch. 2.1 - The function defined by f(x) = sin x has zeros at...Ch. 2.1 - Prob. 1DQCh. 2.1 - Prob. 2DQCh. 2.1 - Is the Bisection method sensitive to the starting...Ch. 2.2 - Use algebraic manipulation to show that each of...Ch. 2.2 - a. Perform four iterations, if possible, on each...Ch. 2.2 - Let f(x) = x3 2x + 1. To solve f(x) = 0, the...Ch. 2.2 - Let f(x) = x4 + 3x2 2. To solve f(x) = 0, the...Ch. 2.2 - The following four methods are proposed to compute...Ch. 2.2 - Prob. 6ESCh. 2.2 - Prob. 7ESCh. 2.2 - Prob. 8ESCh. 2.2 - Use Theorem 2.3 to show that g(x) = + 0.5...Ch. 2.2 - Use Theorem 2.3 to show that g(x) = 2x has a...Ch. 2.2 - Use a fixed-point iteration method to find an...Ch. 2.2 - Use a fixed-point iteration method to determine a...Ch. 2.2 - Use a fixed-point iteration method to determine a...Ch. 2.2 - Prob. 20ESCh. 2.2 - Prob. 21ESCh. 2.2 - a. Show that Theorem 2.3 is true if the inequality...Ch. 2.2 - a. Use Theorem 2.4 to show that the sequence...Ch. 2.2 - Prob. 24ESCh. 2.2 - Prob. 25ESCh. 2.2 - Suppose that g is continuously differentiable on...Ch. 2.3 - Let f(x) = x2 6 and p0 = 1. Use Newtons method to...Ch. 2.3 - Let f(x) = x3 cos x and p0 = 1. Use Newtons...Ch. 2.3 - Let f(x) = x2 6. With p0 = 3 and p1 = 2, find p3....Ch. 2.3 - Let f(x) = x3 cos x. With p0 = 1 and p1 = 0, find...Ch. 2.3 - Prob. 11ESCh. 2.3 - Prob. 12ESCh. 2.3 - The fourth-degree polynomial...Ch. 2.3 - Prob. 14ESCh. 2.3 - Prob. 15ESCh. 2.3 - Prob. 16ESCh. 2.3 - Prob. 22ESCh. 2.3 - Prob. 23ESCh. 2.3 - Prob. 24ESCh. 2.3 - Prob. 25ESCh. 2.3 - Prob. 27ESCh. 2.3 - A drug administered to a patient produces a...Ch. 2.3 - Prob. 30ESCh. 2.3 - Prob. 32ESCh. 2.3 - Prob. 1DQCh. 2.3 - Prob. 2DQCh. 2.3 - Prob. 3DQCh. 2.3 - Prob. 4DQCh. 2.4 - Prob. 6ESCh. 2.4 - a. Show that for any positive integer k, the...Ch. 2.4 - Prob. 8ESCh. 2.4 - a. Construct a sequence that converges to 0 of...Ch. 2.4 - Prob. 10ESCh. 2.4 - Prob. 11ESCh. 2.4 - Prob. 12ESCh. 2.4 - Prob. 13ESCh. 2.4 - Prob. 14ESCh. 2.4 - Prob. 1DQCh. 2.4 - Prob. 2DQCh. 2.4 - Prob. 4DQCh. 2.5 - Let g(x) = cos(x 1) and p0(0) = 2. Use...Ch. 2.5 - Prob. 4ESCh. 2.5 - Prob. 5ESCh. 2.5 - Prob. 6ESCh. 2.5 - Use Steffensens method to find, to an accuracy of...Ch. 2.5 - Prob. 8ESCh. 2.5 - Prob. 9ESCh. 2.5 - Use Steffensens method with p0 = 3 to compute an...Ch. 2.5 - Use Steffensens method to approximate the...Ch. 2.5 - Prob. 12ESCh. 2.5 - Prob. 13ESCh. 2.5 - Prob. 14ES

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