Given a function f(x, y, z) = ryz° +z°yln (z) – z'y? + 4, find: of (1,2, 1) = (1, 2, 1) = (1,2, 1) = azdy (1,2, 1)

Q: Let = (3, 4, 12) . Find the directional derivative of f(z, y, 2) =1– y² +32³ in the direction of v.

A: Consider the given function, fx,y,z=x-y2+3z3 and v=3,4,12 Now, find the derivative of the function…

Q: j Find y as a function of æ if a?y" – 9xy' + 25y = xº, (1) — 2, У(1) — -5. y =

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Q: Find fyyzz if f(x, y, 2) = cos(3y + az). Then evaluate fygazz at point (, 0, 4). COS

A: *Use chain rule

Q: Find the indicated value of the function f(x.y.z) = 3x - 5y? + 9z° - 6. f(9, – 3,1) f(9, - 3,1) = O

A: f(x,y,z)=3x-5y2+9z3-6f(9,-3,1)=3×9-5×((-3)2)+9(13)-6f(9,-3,1)=27-45+9-6f(9,-3,1)=36-51f(9,-3,1)=-15

Q: 29. f(x, y) = x + y, C: x? + y² = 4 in the first quadrant from (2, 0) to (0, 2)

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Q: Q (1): Find fxyz for the function: = xe² + ye* + zey a) f(x, y, z) %3D

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Q: Evaluate F.dr where F(x, v)=xyi (4, 0).

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Q: Find Duf at P. f(x, y, z) = 6x³y³z³; P(2, — 2, 2); u = Duf = i + - 2|3 k

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Q: For the given function 9 = x-yz and 62 -(@C) at C= 3x?yi+ yz²j- xzk, Find 5yöz бубz point (1, – 2, –…

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Q: Q.2 Find DivF and curlF at point (1,2) , where f(x, y) = xy² + Inxy

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Q: Find f(1, 3) and f,(1, 3) for the function f(x, y) = 2x'y² + 2y +4x.

A: Given function is f(x,y)=2x3y2+2y+4x find fx1,3 and fy1,3

Q: Determine Duf(-1,3, 2) for f (x, y, z) = e2ay° + 4x²yz in the direction (3, -2, 5). V =

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Q: Find f, (8,2) if f(x.y) = e* - 5y.

A: We can find the answer as below

Q: If fxy (x, y) = y for 0 2X - 2) =

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Q: Given that Vf(2, -13) = 2i- j, find the directional derivative of the function f at the point (2,…

A: The given problem is to find the directional derivative of the given function at point (2,-13) in…

Q: Determine f„ (0, T, 1), fy(0, , 1), f¿(0, r, 1) given the function z sin(3xz+ y²)

A: The given function,        zsin3xz+y2

Q: 43" + 52y' + 169y = 0, y(0) = 8, 3'(0) = 5.

A: Given that, the differential equation is 4y''+52y'+169y=0 ,y0=5 and y'0=5 . The auxiliary equation…

Q: find Pn (Q'U R).

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Q: What is the probability that both shots will be within 1 meter of the target, in the horizontal…

A: For the random variable X1, Mean, μ1=0Standard Deviation, σ1=0.5 For the random variable X2, Mean,…

Q: Find m such that the function y= Aex satisfies the equation 2y"=y'+y

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Q: Find y as a function of t if 16y" – 72y' + 72y= 0, and y(4) = 9, y' (4) = 8. y =

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