(ii) Let variables x, y and z be linked by the two relationships f(x, y, z) = x³y - z - 1 = 0, g(x, y, z) = x + y² +2³-6=0. Derive conditions on the differentials dx, dy, and dz if the functions f and g are kept at these values. Show that (x, y, z) = (1, 2, 1) is a solution. Use calculus (i.e., by using the expressions for dx, dy, dz) to estimate the corresponding values of x and y when z = 1.1.
(ii) Let variables x, y and z be linked by the two relationships f(x, y, z) = x³y - z - 1 = 0, g(x, y, z) = x + y² +2³-6=0. Derive conditions on the differentials dx, dy, and dz if the functions f and g are kept at these values. Show that (x, y, z) = (1, 2, 1) is a solution. Use calculus (i.e., by using the expressions for dx, dy, dz) to estimate the corresponding values of x and y when z = 1.1.
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter11: Differential Equations
Section11.1: Solutions Of Elementary And Separable Differential Equations
Problem 54E: Plant Growth Researchers have found that the probability P that a plant will grow to radius R can be...
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![(ii) Let variables x, y and z be linked by the two relationships
f(x, y, z) = x³y -z-1=0,
g(x, y, z) = x + y² +2³-6=0.
Derive conditions on the differentials dx, dy, and dz if the functions f and g are kept at these
values. Show that (x, y, z) = (1, 2, 1) is a solution. Use calculus (i.e., by using the expressions for
dx, dy, dz) to estimate the corresponding values of x and y when z = 1.1.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4061eb31-6ba2-4539-9b51-dd7b05481e7e%2Fe3522831-9e51-419c-ba68-262cebb401d6%2F8d2s0p9_processed.png&w=3840&q=75)
Transcribed Image Text:(ii) Let variables x, y and z be linked by the two relationships
f(x, y, z) = x³y -z-1=0,
g(x, y, z) = x + y² +2³-6=0.
Derive conditions on the differentials dx, dy, and dz if the functions f and g are kept at these
values. Show that (x, y, z) = (1, 2, 1) is a solution. Use calculus (i.e., by using the expressions for
dx, dy, dz) to estimate the corresponding values of x and y when z = 1.1.
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