x x² + y² +z²' Hence, find its potential function. Given that F= y x² + y² +3²+y²+z²k ; prove that F is irrotational.

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A:

Q: 5. Find the linear appoximation for the funciton f(x, y) = (ro, Yo) = (3,0). x-y xy+1 at the point

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Q: Let f(x, y, z) = 5x³ - y³ + z². Find the maximum value M for the directional derivative at the point…

A: Our objective is given below:

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Q: Q7. Q7. Consider the vector-valued function 3ry ra(r, y. :) = (V=(* + s°), ) z(2² + y°), r2(r, y, z)…

A:

Q: z= f(x,y) ; x= r-s1 , y= r2s and zx(0,-1) = -24 ; If zx(0,-1)=-18, what is the value of the…

A: Given that z=f(x,y),     zx(0,-1)=-24 and  zy(0,-1)=-18x=r-s and y=r2s We have to find zr(0,-1).

Q: Find a function f such that Vf = 2e²x cos(5y)i - 5e²x sin(5y)j + z³k. f(x, y, z) =

A: Given :-  = 2e2x.cos(5y)i - 5e2xsin(5y) j + z5kNow,

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A: Given that F=x cosx2+y2 i+y cosx2+y2 j. We have to show that F is conservative.For this, let F=F1…

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Q: Let y: (0, 3] → R?, y(t) = (t,?V³) and I := ran y. Sketch T and compute L(T) :!!

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Q: The directional derivative of f(x, y) = √5x + 3y at the point (4,3) in the direction corresponding…

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Q: Compute the discriminant D(x, y) of ƒ(x, y) = x2y2.

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A: The given gradient function

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Q: Let u(t)=6t3i+t2−4j−5k and v(t)=eti+9e−tj−e9tk. Compute the derivative of the following function.…

A: solve the following

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