Suppose you are a bug buzzing around in space. You are currently at the point (1, 1, 0). If the temperature at point (x,y,z) is given by T(x, y, z) = xyz + x²y — z. If you are a bug that likes warm temperatures, which direction should you fly in to move in the direction of most rapid temperature increase? (0, 1, 2) (0, 2,1) (1, 0,2) (1,2,0) (2,0,1) (2, 1,0)

Q: Match each equation on the left with its y = 0 trace on the right.

A: Given,                  x2-y2+z2=-1.

Q: f(x y, z) = x2 - 8y5 + z -4. Find (-3, 1, 5) for O a 1 O b -4 10 O d -5

A:

Q: XI. 6 F dF where F = (x³ – y, x + e') and C is triangle with vertices (0,0), (3,0), (4,2).

A:

Q: The temperature at a point (x, y) on a rectangular metal plate is given by T(x, y) = 100 - 2x2 - y2.…

A: Given: T(x,y) = 100-2x2 -y2We have to find the path a heat-seeking particle will take, starting at…

Q: Iff (x, y) = 4x³ +7y², findf (1,2).f; (1,2).f, (1, 2). f (1, 2) = fx (1, 2) = fy (1, 2) =

A:

Q: Find f, (8,2) if f(x.y) = e* - 5y.

A: We can find the answer as below