Determine if F is conservative, if it is then find a potential function. (a) F =< 2x + ye", 2y + yeª > (b) F =< y,x, z² > (c) F =< cos z, 2y, –x sin z >

Q: Let f(x, y)= x'y+2x² and find f.(1,2) and f,(1,2) %3D 3x- y 1.

A: The given function is: f(x,y)=x2y+2x23x-y

Q: 2. Find the directional derivative of f(x,y) = x cos y in the direction of v = 22, -1). A. (2 cos y…

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Q: Find the local extrema of the function f(x, y) = e-(cos(r)+sin(y)) and test for which are max, min,…

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Q: Find a potential function for F or determine that F is not conservative. F = (cos(z), 16y, -x…

A: The vector field given in the question is: F = &lt;cos(z), 16y, -xsin(z)&gt; Hence, F1 = cos(z), F2…

Q: Find the direction in which the function g(x, y) = cos(xy) decreases fastest at the point (1, pi)

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Domain

In simple mathematics terms, a domain is defined as the space on which all the possible inputs for the function will lie. It can also be expressed as a set of departures for the required function.