Question

By about how much will g(x, y, z) = 3x + xcos z - ysin z + y change if the point P(x, y, z) moves from P0(2,-3,0) a distance of ds = 0.3 unit toward the point P1(0,-1,2)?

Answer 1

The function g(x, y, z) will change by -3 units when the point P(x, y, z) moves towards P1(0,-1,2) from P0(2,-3,0) a distance of 0.3 units.

Step-by-step explanation:

To find how much the function g(x, y, z) = 3x + xcos z - ysin z + y will change when the point P(x, y, z) moves from P0(2,-3,0) a distance of ds = 0.3 unit toward the point P1(0,-1,2), we need to find the change in the function value at P0 and P1.

Substituting the coordinates of P0 and P1 into the function g(x, y, z), we get g(2,-3,0) = 6 and g(0,-1,2) = 3.

Therefore, g will change by -3 units when P moves from P0 to P1.