Consider the vector field f(x, y,z)=(4z+5y)i+(4z+5x)j+(4y+4x)k. a. find a function f such that f=∇f and f(0,0,0)=0.

The gradient of a function f, denoted as ∇f , is the collection of all its partial derivatives into a vector.

Function  

Gradient of vector field is given by,

And function is given that,

Since,      f = ∇f

After comparing, We get

After observing above equations,

We have,  

Since, , So that,

Thus,  

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answer: expected value of x = 1.0

step-by-step explanation:

p(x=0) = 0.25

p(x=1) = 0.50

p(x=2) = 0.25

expected value for x = 0×0.25 + 1×0.5 + 2×0.25 = 1.0

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step-by-step explanation: