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…

A:

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: f(r,t) = cos(3r) exp(4t) %3D fi(x,t)+ frz(x,t) = f(r,t) %3D

A:

Q: af dy of f(x, y) = tan (x²y³ + 2xy)? What is the

A: Given:     To determine:

Q: Find the directional derivative of f(x, y) = cos(x) + y² at (T,2) in the direction of (3, –4).

A:

Q: 8. Find the directional derivative off at the p in the direction of v = () of f(x, y, z)=x²exx, p =…

A:

Q: Let f(x, y) = x sin ry. Find: fyy (x, y) fyz(x, y)

A: f(x,y)=xsinxyfx=sinxy+xycosxyfyx=xcosxy+x(cosxy-xysinxy)=2xcosxy-x2ysinxyfy=x2cosxyfyy=-x3sinxy

Q: Let f(x, y) = x2 – y?. Find (a) The directional derivative of f at (-2, 1) in the direction of v = i…

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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: I need the answer as soon as possible

A: As we know that, eiz=cosz+isinz                   ...(1)And,e-iz=cosz-isinz                ....(2)…

Q: 7. Which of the following sets of functions is linearly dependent on R0,2? (a) {6, z, sinz} (b) {1,…

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Q: Find the directional derivative of the function f(x, y, z) = 3e" sin(xy) in the direction of v = 3i…

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Q: iv is analytic = -11..

A:

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

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Q: af If f(x,y) = sin-(4x³y?) then dx 12x?y? 1-(4x³y²)² O a. b. 1 4x³y²/(4x³y?)² – 1 c. 12x²y² 4x³y?…

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Q: Q3 Find the directional derivative of f(x,y,z)=xy+yz+zx at the point (1,-1,2) in the direction of A…

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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.