Find the directional derivative of the function at the given point in the direction of the vector v. f(x, y, z) = xe^y + ye^z + ze^x, (0, 0, 0), v = 4, 3, −2

Step-by-step explanation:

We need to find the directional derivative of the function at the given point in the direction of the vector v.

,point (0, 0, 0) and

By Theorem: If f is a differentiable function of x , y and z , then f has a directional derivative for  any unit vector and

where

since,  

then

The partial derivatives are

Then the directional derivative is

so, directional derivative at point (0,0,0)

a) one student is chosen from classroom a, then a student is chosen from classroom b.  

step-by-step explanation:

independent events are ones in which the probability of one event does not affect the probability of the second event.

one student is chosen from classroom a; this does not affect the chances of choosing a student from classroom b.   this makes these independent events.

when one card is chosen from a standard deck and then set aside before a second card is chosen, the probability of the second card being chosen changes.   this makes them dependent events.

when one student is chosen from classroom a and then a second student is chosen from classroom a, the probability of choosing the second student changes.   this makes them dependent events.

when a letter is chosen from the alphabet and then a second letter is chosen, the probability of choosing the second letter changes.   this makes them dependent events.

step-by-step explanation: