Find that F = 12x²yi + (4x + 8yz²)j + 8y² zk is conservative, and find a function f such that F = Vf, and use the result to evaluate F • dr, where C is any curve from A = (0, 0,0) to B = (-3,2, 3).

Q: Find and classify all stationary points of the function f(x,y) = x³ + xy + y² − x.

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Q: Find (url and dive rgence the of F(xy2)=Xy2 i+ 2x Y j t z(os xyk.

A: Given: F(x, y, z) = xyz i + 2xy j + 2cosxy k To find: Curl and divergence of the given function.

Q: F=(x-y², x²•y +3) at A-(1, 1), B=(2, –1) and C=(0,-2). %3D

A: The divergence of a vector field F = <P,Q> is defined as the partial derivative of P with…

Q: Consider the function f(x) = In (x - 4) a.) Use the First Derivative Test or the Second Derivative…

A:

Q: Verify that ƒxy = ƒyx, for ƒ(x, y) = xey.

A: Given function is fx,y=xey We have to verify fxy=fyx Solution: fxy means that first we find partial…

Q: Calculate fz(3, 6, 9), where f(x, y, z) = xyz. fz(3, 6, 9) =

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Q: Give two distinct linear functions ƒ and g that satisfy ƒ'(x) = g'(x); that is, the lines have equal…

A: It is given that fx and gx two distinct function.

Q: 7] Sketch a graph of the function below. Include calculations of all key features. 1 f(x) : ーx-3 %3D…

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Q: Find the gradient of f(m, n) = m³ +n³. grad f = i +

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Q: Consider an F-curve with d f = (2, 14). Determine F0.05.

A: The F-curve 0.05 area with degrees of freedom 2 and 14.

Q: Compute ƒxxx and ƒxxy for ƒ(x, y) = x3y.

A: Given function - f(x, y) = x3yConcept - While partially differentiating with respect to x, other…

Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as: