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 15.1, Problem 2E
To determine
The approximate solution of Laplace’s equation at the interior points of the region
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In Problems 17–36, use Theorem 2 to find the local extrema.
Problem 9. Find a parametrization of the curve of intersection of x = √y and z = √y from (1, 1, 1) to
(4, 16, 2).
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Question 17
Find a parameterization for the line segment from (2, –1) to (-6, 4).
a) O (t) = -1– 5t and y (t) = 2 + 8 t, t e [0, 1]
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b) O (t) = -1+ 5t and y (t) = 2 – 8 t, t E [0, 1]
c)
a (t) = 2 + 8 t and y (t) = -1- 5 t, te [0,1]
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d) O a (t) = -2 + 8t and y (t) = 1 – 5 t, t E [0,1]
O a (t) = 2 8t and y (t) = -1+ 5t, te [0, 1]
f) O None of the above.
Review La
Question 18
Chapter 15 Solutions
Differential Equations with Boundary-Value Problems (MindTap Course List)
Ch. 15.1 - In Problems 14 use (5) to approximate the solution...Ch. 15.1 - Prob. 2ECh. 15.1 - Prob. 3ECh. 15.1 - Prob. 4ECh. 15.1 - In Problems 5 and 6 use (6) and Gauss-Seidel...Ch. 15.1 - In Problems 5 and 6 use (6) and Gauss-Seidel...Ch. 15.1 - (a) In Problem 12 of Exercises 12.6 you solved a...Ch. 15.1 - Use the result in part (a) of Problem 7 to...Ch. 15 - Consider the boundary-value problem...Ch. 15 - Solve Problem 1 using mesh size . Use Gauss-Seidel...
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- QUESTION 3 31 in the diagram befow line seument AB mtersects ine egnt OC and a the size of r ond y (4) (a) DCE (3) (b) 150 20 120 (c) Zx-20 80 (d) Find the values of x, y and z if Ab//Cd. 120arrow_forward2. A bug is crawling along the surface defined by x³ + y²z – z³ = 5. The bug is currently at the point (2, –2, –1). (a) If the bug moves along the surface by increasing its y-coordinate and keeping x = quickly is its z-coordinate changing? = 2, then how (b) If, instead, the bug moved from (2, –2, –1) along the surface by increasing its z-coordinate, and keeping y = -2, then how quickly is its x-coordinate changing?arrow_forwardProblem 5. Find and Classify the critical point of (x,y)=192x³+y²–4xy² on the triangle with vertices (0,0), (4,2) and (-2,2).arrow_forward
- Ex. 5. Find a solution of Laplace's equation, u +u„ =0, inside a rectangle subject to the following boundary conditions: а. и(0, у) 3 0, и(, у) 3 0, и(х,0) — -4sin (2rx). и(х,5) %3 6sin (3rx). b. и(0), у) - 0, и(, у) - 0, и(х,0) —х', и(x,2) -0. с. и, (0, у) 3 5sin (ту). и,(1, у)-13sin (2тy), и(х,0) — 0, и(х,2)-0. d. u, (0, у) — 0, и(1, у) — 0, и(х,0) —0, и, (х, 2) %35 сos 2 е. и, (0, у) - 0, и, (2л, у) - 0, и(х,-1)-0, и(х,) —1+sin (2xх).arrow_forwardProblem 1. Evaluate the circulation of G = ryi + zj + 2yk around a square of side 7, centered at the origin, lying in the yz-plane, and oriented counterclockwise when viewed from the positive x-axis. F. dr = Circulation =arrow_forward13. The standard form of 3dy-xydx = 3y3e4x/3 by Bernoulli's equation is:arrow_forward
- 8. Evaluate •S.F.d F-dr where F(x, y, z) = (-7 sin(7x)-yz, π cos(ny)-xz, -xy) and C is any path that starts at (1,1/2,2) and ends at (2,1,-1). (a) 4 (b) 5 (c) 6 (d) 7 (e) 8arrow_forwardWhich of the following is NOT a possible solution for Laplace's equation? (a) y = (AePx + Be-P*)(Ccos py + Dsin py) (b) y = (Acos px + Bsin px)(CEPY + De PY) (c) y = (Ax + B)(Cy + D) (d) y = (A P* + Be-P*)(CePy + Depy) O a O b O carrow_forwardProblem 6. Use a change of variables to evaluate JJ cos(y+ x) dA, where P is the parallelogram bounded by 2x + y = 1, 2x + y = 5, 3x y = 2 and 3x - y = -3. 3 2 0arrow_forward
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