Differential Equations with Boundary-Value Problems (MindTap Course List)
9th Edition
ISBN: 9781305965799
Author: Dennis G. Zill
Publisher: Cengage Learning
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Chapter 9.2, Problem 20E
To determine
The number of evaluations of a function
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A student solves an optimization problem as in Model 1, except that in the problem Mini and
Max are given 800 feet of caution tape. Examine the student's solution, explain what they did
wrong, and write down what the student should have done instead.
Student Solution (find the error):
A=xy
P = 2x+2y = 800
400 - x = y
A = x (400-x) = 400 x - x²
A'(x) = 400 2x, so x = 200 is a critical number.
Check the endpoints (x = 0 and x = 400) and critical number:
A'(0) = 400; A'(200) = 0; A'(400) = -400.
Therefore the maximum area is 400 square feet.
The number of defects on the front side (X) of a wooden panel and the number of defects on the rear side (Y) of the panel are under study. Suppose that the joint pmf of X and Y is modeled as fxy (x,y)=c(x+y), x=1,2,3 and y=1,2,3. Check if the number of defects on the front side (X) of a wooden panel and the number of defects on the rear side (Y) of the panel are independent.
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min
f(x1, x₂) = ₁x₂ + 4x₁+x²23
s.t.
x1 + 2x₂ > 20
I1, I2 > 0.
Chapter 9 Solutions
Differential Equations with Boundary-Value Problems (MindTap Course List)
Ch. 9.1 - In Problems 110 use the improved Eulers method to...Ch. 9.1 - In Problems 1–10 use the improved Euler’s method...Ch. 9.1 - In Problems 1–10 use the improved Euler’s method...Ch. 9.1 - In Problems 1–10 use the improved Euler’s method...Ch. 9.1 - Prob. 5ECh. 9.1 - Prob. 6ECh. 9.1 - In Problems 1–10 use the improved Euler’s method...Ch. 9.1 - In Problems 1–10 use the improved Euler’s method...Ch. 9.1 - Prob. 9ECh. 9.1 - Prob. 10E
Ch. 9.1 - Prob. 11ECh. 9.1 - Prob. 13ECh. 9.1 - Prob. 14ECh. 9.1 - Prob. 15ECh. 9.1 - Prob. 16ECh. 9.1 - Consider the initial-value problem y = 2x 3y + 1,...Ch. 9.1 - Prob. 18ECh. 9.1 - Prob. 19ECh. 9.1 - Repeat Problem 19 using the improved Euler’s...Ch. 9.1 - Prob. 21ECh. 9.2 - Use the RK4 method with h = 0.1 to approximate...Ch. 9.2 - Prob. 2ECh. 9.2 - Prob. 3ECh. 9.2 - Prob. 4ECh. 9.2 - Prob. 5ECh. 9.2 - Prob. 6ECh. 9.2 - Prob. 7ECh. 9.2 - Prob. 8ECh. 9.2 - Prob. 9ECh. 9.2 - Prob. 10ECh. 9.2 - In Problems 312 use the RK4 method with h = 0.1 to...Ch. 9.2 - Prob. 12ECh. 9.2 - Prob. 13ECh. 9.2 - Consider the initial-value problem y′ = 2y, y(0) =...Ch. 9.2 - Prob. 17ECh. 9.2 - Consider the initial-value problem y′ = 2x – 3y +...Ch. 9.2 - Prob. 19ECh. 9.2 - Prob. 20ECh. 9.3 - Prob. 1ECh. 9.3 - Prob. 3ECh. 9.3 - Prob. 4ECh. 9.3 - Prob. 5ECh. 9.3 - Prob. 6ECh. 9.3 - Prob. 7ECh. 9.3 - Prob. 8ECh. 9.4 - Use Euler’s method to approximate y(0.2), where...Ch. 9.4 - Prob. 2ECh. 9.4 - Prob. 3ECh. 9.4 - Prob. 4ECh. 9.4 - Prob. 5ECh. 9.5 - Prob. 1ECh. 9.5 - Prob. 2ECh. 9.5 - Prob. 3ECh. 9.5 - Prob. 4ECh. 9.5 - Prob. 5ECh. 9.5 - In Problems 1-18 use Definition 7.1.1 to find ℒ{f...Ch. 9.5 - Prob. 7ECh. 9.5 - Prob. 8ECh. 9.5 - Prob. 9ECh. 9.5 - Prob. 10ECh. 9.5 - Prob. 11ECh. 9.5 - The electrostatic potential u between two...Ch. 9.5 - Consider the boundary-value problem y″ + xy = 0,...Ch. 9 - Prob. 1RECh. 9 - Prob. 2RECh. 9 - In Problems 1–4 construct a table comparing the...Ch. 9 - In Problems 1–4 construct a table comparing the...Ch. 9 - Prob. 5RECh. 9 - Prob. 6RECh. 9 - Prob. 7RECh. 9 - Prob. 8RE
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