Determine D„f(4, –1,6) for f(x,y,z) = ex³y + 4zx³ in the direction of (–3,2,6). %3D

Q: 2. Show that the function u = p(xy) + Vry v(y/x) provides the equation = 0. dy? | dx²

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Q: Compute dy and ∆y for y = sqrt(x^3 + 1) for the change in x from x = 2 to x = 2.03. Is dy a good…

A: According to the given information, it is required to determine dy and Δ(y) for the given function…

Q: Find the direction at which the function f(x, y, 2) = a In(e-az) increases fastest at (-3,0, 0) O…

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Q: Use the linear approximation to f (x, y) = √x/y at (9, 4) to estimate √9.1/3.9.

A: f(x,y)=xy at (9,4) to estimate 9.13.9

Q: Find the linearization at x = a. IT f(x) = sin³ (x), a = 4

A: Given,            The linearization at x=a.             fx=sin3x, a=π4We know that,             The…

Q: Where f(x, y) y calculate (–1, 1) towards the point dv (-1, 3)

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Q: af Find a d () + In (). of the function f(x,y) = arccot and ду

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Q: O Find the directional derivative of f(x, y) = 3x² – 3y² in the direction from P(-,0) to Q(0, 1).

A: Point is given so first find the direction unit vector then  dot product with divergent of f(x,y)…

Q: Show that S f(x,y) dy dx = , f(x,y) dx'dy. %3D

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Q: F(X, y,z) = 2x -y? +z?

A: F(x,y,z)= 2x-y^2-z^2 at point (4,-4,2) df/dx= 2 df/dy=-2y df/dz= -2z

Q: Find fr and fy- S(x, y) = /"9e" dt f.(r, y) : %3D f,(x, y) =

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Q: Q4/ Find the direction in which the function f(x,y) = /xy² + 1 increases most rapidly at P-(1,-1)…

A: Here we will differentiate f(x,y) with respect to t and solve this question.

Q: Calculate fxxyz for f (x, y, z) = y sin(x + z).

A: We first differentiate the given function with respect to x twice. Then y and z will be treated as…

Q: 2, 0 1

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Q: Use the Linear Approximation to f(x, y) = x/y at (9, 4) to estimate 9.1/3.9.

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Q: Find the direction at which the function f(x, y, z) = x In(e – az) increases fastest at (-3,0, 0) O…

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Q: The equation of line normal to f(x) = (x +4)^(1/2) at Q (0,3) is

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Q: 2. Show that the function u p(ry) + Vry v(y/x) provides the equation Pu = 0. ду? dx²

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Q: Calculate fxxyz for f(x, y, z) = y sin(x + z).

A: For a function in several variables, partial derivative with respect to one variable say x can be…

Q: Integrate f(x, y)

A: The region is defined as, Consider the conversion formulae from cartesian to polar coordinates,…

Q: J f(x)dx = f(x)dx =7, then J f(x)dx = If 4 and

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Q: 1 F (s) = s (s +1) %3D

A: Given: L-11ss+1

Q: dx Show that f - In|ax + b| + C where a # 0. ax+b

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Q: Which direction is the directional derivative of the function f (x,y, z) = x2 – 2yz at point…

A: Solution: The function is fx,y,z=x2-2yz The point is P1,1,1 We have to find the direction in which…

Q: Q2 / Find the directional derivative of f(x.y.z) 4xy +5xz2 +6yz2 At the point P(3,1,4) in the…

A: ∂f∂x=4y+5z2∂f∂x=84∂f∂y=4x+6z2∂f∂y=108∂f∂z=10xz+12yz∂f∂z=168Therefore, the gradient is∇f (3, 1, 4)…

Q: 2. Show that the function u = p(xy) + Vry ý(y/x) provides the equation n, = 0. dy? U -

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Q: Compute fe F d where F (x, y) = x² + y). (2xy + x, Hint: Is F conservative?

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Q: Find fr and fy- f(x, y) = 7e dt f-(x, y) = f,(x, y) =

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Q: Evaluate 3rz dV where E = {(x,y, z) | 2 <r < 5, a <y < 2r, 0 < z< +3y}. %3D Round your answer to…

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Q: In integrating the function fx* in Sx dx using integration by parts, what would you choose for your…

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Q: 2 Find f, fyand f. if f(x, y, z) = x-Vy + z°

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Q: Find fy(x,y) and fy(x,y). Then, find fy(- 3,1) and fy(1, – 4). f(x,y) = In |7 + 4x°y²|

A: Let f(x,y) be the given function .Then fx is the derivative of f with respect to x  , treating y as…

Q: Let f(x, y) = 6e sin(7y) af af dy

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Q: Integrate the function f (z) = (z – 8i)² from z = 0 to z = 4 + 4i along the line x = y. 2

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Q: Find fr and fy. 2e" dt f (x, y) = 2, f.(r, y) = f„,(x, y) =

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Q: Let f(x, y) = 7e2" sin(5y) af af dy

A: We can make it easier for you

Q: - x'yt, show that fxy = fyx. 7,4 Given f(x, y) = et*

A: Given f(x,y) = e(x^4y^9) - x7y4

Q: Find the particular sölution f"(x) = 4, f'(2) = 12, f(2) = 17

A: integration 2 times and after applying initial condition we get f(x)

Q: Find fy (X,y) if f(x,y) = (x° + y°)°. ху Exy(x.y) =

A: Topic: differentiation

Q: Find fyy for f(x, y) = e* In(y).

A: The given function is fx,y=exlny.

Q: 8y If the directional derivative of f(x,y)D at (2,1) in the direction of (a, 2) is equal to zero,…

A: Given,            f(x,y)=8yx

Q: 14. If X has the PDF f(r) = 1/4, -1<r<3, zero elsewhere, find the PDF of Y %3D

A: Given,f(x)=14  ; -1&lt;x&lt;3Y=X2

Q: D SS f(x,y,z) dV = f(x,y,z) dx dy dz

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Q: Find f-(x, y) and fy(x, y). f(1, y) = (y^tan(4x)) fa(x, y) : fo(x, y)

A: The given function is: f(x,y)=y5 tan(4x)-43

Q: Show that f(x.y) dy dx= ,f(x,y) dx dy. ||

A: Order of change of integrals

Q: Find fr and fy- f(x, y) = fetlo dt f.(r, y) = fy(x, y)

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Q: f(x, y) = /32² + 3y fz(4, 5) = VT23 %3D

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Q: 4) f(x,y) =Vx +y Ans. f.= +y Vx + y?

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Q: Find the direction at which the function f(x, y, z) = x In(e' – xz) increases fastest at (-3,0, (0,…

A: Sorry I cannot recognize your given points. So I provide only methods of problem you can easily…

Q: Use the linear approximation to ƒ(x, y) 12x² at (3, 9) to estimate f(3.1, 8.8). y2+7 (Use decimal…

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