Question

use f(x, y, z) = x^2 + yz, f(x, y, z) = [xy, yz, xz], and g(x, y, z) = (−sin(z), exz, y) . compute (f ✕ g)(2, −1, 8).

Answer 1

To compute (f ✕ g)(2, −1, 8), we need to find the values of f(2, −1, 8) and g(2, −1, 8), and then multiply them together.

Step-by-step explanation:

To compute (f ✕ g)(2, −1, 8), we need to find the values of f(2, −1, 8) and g(2, −1, 8), and then multiply them together.

From the given information, we know that f(x, y, z) = x^2 + yz and g(x, y, z) = (−sin(z), exz, y).

Substituting the values x = 2, y = −1, and z = 8 into f(x, y, z) and g(x, y, z), we can calculate f(2, −1, 8) and g(2, −1, 8).

Finally, we multiply f(2, −1, 8) and g(2, −1, 8) to find (f ✕ g)(2, −1, 8).

Answer 2

To compute (f x g)(2, -1, 8), we first find f(2, -1, 8) and g(2, -1, 8) by substituting the values. Then we multiply the corresponding components of f and g to get (f x g)(2, -1, 8).

Step-by-step explanation:

To compute the expression (f x g)(2, -1, 8), we need to first calculate f(2, -1, 8) and g(2, -1, 8).

For f(x, y, z) = x^2 + yz, we substitute x=2, y=-1, and z=8 to get f(2, -1, 8) = 2^2 + (-1)(8) = 4 - 8 = -4.

For g(x, y, z) = (-sin(z), exz, y), we substitute x=2, y=-1, and z=8 to get g(2, -1, 8) = (-sin(8), e(2)(8), -1) = (-sin(8), e^16, -1).

Finally, we compute (f x g)(2, -1, 8) by multiplying corresponding components: (f x g)(2, -1, 8) = (-4)(-sin(8), -4e^16, 4) = (4sin(8), 4e^16, -4).