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13. f(x, y) = x cos y (x +y)(xy- I 16. f(x, y) = (x + y)(xy – IJ 15. f(x, y) = x sin (x + y) 17. Find the shortest distance from the point (2, 0, 3) to the plane x - y+z = 4. 1/xy and the origin. 17. 18. Find the shortest distance between the surface z 19. Find the dimensions of a closed, rectangular box of given volume V > 0 that has minimum surface area. 20. Find the point(s) on the surface xyz +1 = 0 that are closest to the origin. 21. Find the volume of the largest (i.e., of maximum volume) rectangular box that can be inscribed into the sphere of radius R > 0. 22. Suppose that you have to build a rectangular box (with a lid) using S > 0 units´ of material. Find the dimensions of the box that has the largest possible volume. 23. It was shown that the function g(x, y) = x* – yª of Example 4.28 has a saddle point at (0, 0). Draw the contour curve that goes through (0, 0). Add a few more level curves to your picture. 24. Find all points where the magnitude of the vector field F = (x – y)i + (2x + y + 3)j attains its local minimum. 25. A plane in a three-dimensional space, which is not parallel to any of the three coordinate planes, can be analytically described using the equation x /a +y/b+ z/c = 1, where a, b, and c are bectively. Find the plane that passes through (1, 1, 1) %3D its x-intercept, y-inter and z-interc and is such that the e firs led by that plane has the smallest volume. E- 26 am an e maximum of a given function f(x, y) riangula vertices (0, 0), (2, 0), and (0, 2) s the trian vith vertices (0, 0), (1, 0), and (1, 1)

13. f(x, y) = x cos y (x +y)(xy- I 16. f(x, y) = (x + y)(xy – IJ 15. f(x, y) = x sin (x + y) 17. Find the shortest distance from the point (2, 0, 3) to the plane x - y+z = 4. 1/xy and the origin. 17. 18. Find the shortest distance between the surface z 19. Find the dimensions of a closed, rectangular box of given volume V > 0 that has minimum surface area. 20. Find the point(s) on the surface xyz +1 = 0 that are closest to the origin. 21. Find the volume of the largest (i.e., of maximum volume) rectangular box that can be inscribed into the sphere of radius R > 0. 22. Suppose that you have to build a rectangular box (with a lid) using S > 0 units´ of material. Find the dimensions of the box that has the largest possible volume. 23. It was shown that the function g(x, y) = x* – yª of Example 4.28 has a saddle point at (0, 0). Draw the contour curve that goes through (0, 0). Add a few more level curves to your picture. 24. Find all points where the magnitude of the vector field F = (x – y)i + (2x + y + 3)j attains its local minimum. 25. A plane in a three-dimensional space, which is not parallel to any of the three coordinate planes, can be analytically described using the equation x /a +y/b+ z/c = 1, where a, b, and c are bectively. Find the plane that passes through (1, 1, 1) %3D its x-intercept, y-inter and z-interc and is such that the e firs led by that plane has the smallest volume. E- 26 am an e maximum of a given function f(x, y) riangula vertices (0, 0), (2, 0), and (0, 2) s the trian vith vertices (0, 0), (1, 0), and (1, 1)

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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13. f(x, y) = x cos y (x +y)(xy- I 16. f(x, y) = (x + y)(xy – IJ 15. f(x, y) = x sin (x + y) 17. Find the shortest distance from the point (2, 0, 3) to the plane x - y+z = 4. 1/xy and the origin. 17. 18. Find the shortest distance between the surface z 19. Find the dimensions of a closed, rectangular box of given volume V > 0 that has minimum surface area. 20. Find the point(s) on the surface xyz +1 = 0 that are closest to the origin. 21. Find the volume of the largest (i.e., of maximum volume) rectangular box that can be inscribed into the sphere of radius R > 0. 22. Suppose that you have to build a rectangular box (with a lid) using S > 0 units´ of material. Find the dimensions of the box that has the largest possible volume. 23. It was shown that the function g(x, y) = x* – yª of Example 4.28 has a saddle point at (0, 0). Draw the contour curve that goes through (0, 0). Add a few more level curves to your picture. 24. Find all points where the magnitude of the vector field F = (x – y)i + (2x + y + 3)j attains its local minimum. 25. A plane in a three-dimensional space, which is not parallel to any of the three coordinate planes, can be analytically described using the equation x /a +y/b+ z/c = 1, where a, b, and c are bectively. Find the plane that passes through (1, 1, 1) %3D its x-intercept, y-inter and z-interc and is such that the e firs led by that plane has the smallest volume. E- 26 am an e maximum of a given function f(x, y) riangula vertices (0, 0), (2, 0), and (0, 2) s the trian vith vertices (0, 0), (1, 0), and (1, 1)
Transcribed Image Text:13. f(x, y) = x cos y (x +y)(xy- I 16. f(x, y) = (x + y)(xy – IJ 15. f(x, y) = x sin (x + y) 17. Find the shortest distance from the point (2, 0, 3) to the plane x - y+z = 4. 1/xy and the origin. 17. 18. Find the shortest distance between the surface z 19. Find the dimensions of a closed, rectangular box of given volume V > 0 that has minimum surface area. 20. Find the point(s) on the surface xyz +1 = 0 that are closest to the origin. 21. Find the volume of the largest (i.e., of maximum volume) rectangular box that can be inscribed into the sphere of radius R > 0. 22. Suppose that you have to build a rectangular box (with a lid) using S > 0 units´ of material. Find the dimensions of the box that has the largest possible volume. 23. It was shown that the function g(x, y) = x* – yª of Example 4.28 has a saddle point at (0, 0). Draw the contour curve that goes through (0, 0). Add a few more level curves to your picture. 24. Find all points where the magnitude of the vector field F = (x – y)i + (2x + y + 3)j attains its local minimum. 25. A plane in a three-dimensional space, which is not parallel to any of the three coordinate planes, can be analytically described using the equation x /a +y/b+ z/c = 1, where a, b, and c are bectively. Find the plane that passes through (1, 1, 1) %3D its x-intercept, y-inter and z-interc and is such that the e firs led by that plane has the smallest volume. E- 26 am an e maximum of a given function f(x, y) riangula vertices (0, 0), (2, 0), and (0, 2) s the trian vith vertices (0, 0), (1, 0), and (1, 1)
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