dz dz and at the point (3, 6, 1) where z is defined implicitly by the equation z4 + z?x2 - y - 4 = 0. Calculate ax ду az дх 1(3, 6, 1) az ду Г(з, 6, 1)

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

A: Given that fx,y,z=ex2y+4zx3 Then  ∇f=∂∂xi+∂∂yj+∂∂zkex2y+4zx3=2xyex2y+12zx2i+x2ex2yj+4x3k

Q: The distance from (6,-5, 1) to yZ-plane is OA 6 /26 OC 1 O D. 62 OE 5 В.

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Q: Solve for x, y, z and w. (Enter your ansv x + y y + z 3 5 z + w 8 5 (x, y, z, w) =

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Q: А Q(1, 1) в Q(2, 0) vyQ(1, y) 3xQ(x, 2)

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Q: Solve Utt (1,4) Ux (o,t) =o UCX, 0) = 0 KUXX (xst) 0Lxo %3D Ux (1,t) = 0 Ut (x,0)= 2 %3D -1 %3D…

A: The given problem is to find the solution for the given wave equation partial differential equation…

Q: Sz sec2ysin4ydy

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Q: Calculate the distance from point s(10, -8, 10) to the plane 2x + 2y + z = 4 O 10 O 10 의 ~m 의 29

A: Given query is to find the distance between the plane and point. The given point is S(10, -8, 10)…

Q: OF(2,9)= OF(2,9)= %3D OF (2,y) = X,Y %3D OF(2,y) =

A: Since     F→(x,y)=<-y, x2> The vector field of the function is

Q: 4. If A = 3xyz²i + 2xy³j- x²yzk and p = 3x² - yz, find (a) V-A, (b) A-V4, (c) V-(Vo) at point (1,-1,…

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Q: Determine the location of a point (x, y, z) that satisfies the condition y < 0

A: With the given condition there are 4 scenarios 1) x>0,y<0,z>0 2) x<0,y<0,z<0 3)…

Q: (1,1) = H dy =1(2y - y*)3 - y*| dy =, (8y* – 12y* + 6y5 - y6 – y")dy =(8y - 12y' +6y" – 2y) dy =(4y…

A: Ix and Iy denotes inertia about x-axis and y-axis  Ix=∫∫Ay2 δ(x,y)dA  and Iy=∫∫Ax2δ(x,y)dA And…

Q: Eliminate the parameter from x = 2sint, y=4cost

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Q: Use Cramer's rule to solve for y without solving for x, z, and w. 4x + y w = 3 5x + 2y 4 4x 2 y 5z +…

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Q: If x,+iy,=x,+iy2 then x=y, %3D

A: TRUE for part (1) It is given that x1+iy1=x2+iy2. x1+iy1 and x2+iy2 are complex numbers Two complex…

Q: Solve using method of variation of parameter: 4y" - y = xex/2, y(0) = 1, y'(0) = 0.

A: Let us consider a second order differential equation with constant coefficient , y''+ay'+by=Q(x) To…

Q: I. Determine la ecuación del plano tangente a la superficie dada en el punto especificado 1. z = 4x2…

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Q: Consider a closed rectangular box with dimensions xx  ft by  yy  ft by zz ft. If xx  is increasing…

A: Proceed as shown

Q: If A = 3xyz²i + 2xy³j-x²yzk and p = 3x² - yz, find (a) V-A, (b) A-Vq, (c) V.(Vo) at point (1,-1, 1).

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Q: Differentiate, and make sure to show all your work: y = exin(2z) %3D

A: The given question is taken from the derivative of the function in which we have to find the…

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: This question is from partial differential equation please sir g give me answer immediately

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Q: Determine una ecuación del plano tangente a la superficie dada en el punto especificado *:(-4, 2,…

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Q: Find and determine type of stationary point for ƒ(x,y)=x' – 3x² + 2xy – y

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Q: Find SV. T. 15 30 R U 16 V SV %3D Submit

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Q: Distinguish briefly the Skewness and kurtosis

A: Skewness is a measure of symmetry where symmetry means equal proportion to the left and right to the…

Q: O Civen w (2-31, XL-4,9),Y(S,y) and z(-1,1) find the Value so that ux LYZ

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Q: A particle moves along a circular path over a horizontal xy coordinate system, at constant speed. At…

A: Given Motion is a circular motion. r = radius of the circlea = x-cordinate of the centreb =…

Q: Find Duf at P. 1 2. f (x, y, z) = 6x³y°z°; P(2, – 2, 2); u %3D - -

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Q: Given f(x, y, z) = /2x – y – 5z, find - - f-(x, Y, z) = %3D f,(x, Y, 2) = %3D f-(x, Y, z) =

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Q: Question 2: Determine Duf(4, –1,6) for f(x, y, z) = e*³y + 4zx³ in the direction of (–3,2,6). %3D…

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Q: If A = 2.x2i – 3yzj+xz²k and o = 2z – x°y, find A.Vø at the point (1, –1, 1). |

A: The gradient is calculated using the del operator and it can be represented as ∇=∂∂xi^+∂∂yj^+∂∂zk^.…

Q: If A = 2x2'i– yzj +3xz'k and ø=x³yz, find V×(ø4)at the point (1, 0, -1).

A: Given A = 2xz2i - yzj + 3xz3k and  ϕ = x2yzSo, ϕA=  x2yz(2xz2i - yzj + 3xz3k)     =  2x3yz3i…

Q: Determine D,f (4,-1,6) for f(x,y,z) = ery + 4zx in the direction of (-3,2,6).

A: Given fx,y,z=ex2y+4zx3 in the direction of -3,2,6

Q: 3. If V = (3r'y-1,x2'+y',-2r:"). Find grad divl at the points (2,-1,0).

A: We have to find grad(divV ) at (2,-1,0) where  V = (3x2y-z,xz3+y4,-2x3z2)

Q: Rule: (x, y) → ( Reflection: Across Line y = x

A: Actually the rule of reflection along y=x is simply writing the points (x,y) as (y,x). See for the…

Q: 3. Find how many roots the equation 2z4 – 323 + 3z² – z + 1 = 0 - - has in the right half-plane Rez…

A: Given: 2z4-3z3+3z2-z+1=0

Q: Solve Utt currrx = 0, -0 0, %3D u (x,0) = f (x), Ut (x,0) = 0, -0 < x < ∞ ||

A: Given that,utt+c2uxxxx=0-∞&lt;x&lt;∞t&gt;0ux, 0=fxutx, 0=0The pde is solved as shown below

Q: If ø(x, y, z) = ry²z find grad ø at (2, – 1, 3).

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Q: Compute (x² + 2y + 3z +1) ds where Cis the line segment from (0, 2, 3) to (2, 5, 7).

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Q: 27 hPlans that pas Ses through the Point C60,27 and contains the like メt4-2t)ソ= 34st) Zzス+4t 7.

A: Recall: General equation of a plane :     An equation for the plane through (x0, y0,z0 ) and…

Q: az Find at (2, -2, 1) if x2 + y? + z2 = 6xz+ 6yz + 21 %3D 8. %3D %3D dy %3D 25 25 1.

A: Given,x2 + y2 + z2 = 6xz + 6yz + 21

Q: Calculate Duf(0,–2,5) in the direction of v = -3i + 12j – 4k for the function f(x,y,z) = 3x² + xy –…

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Q: An unevenly heated metal plate has temperature T(x,y)T(x,y) in degrees Celsius at a point…

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Q: By means of Lagrange's formula, prove that 1 Yo = - 1 - [2 (y₁+y_₁). (Y3 - y₁) 2 -Y₁) - 2 (Y-₁-y-3)…

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Q: Suppose that z = f(x,y), find for 4 x²z* – 5yz³ + xy? - 3z? = x

A: Given: 4x2z4−5yz3+xy2−3z2=xz=f(x,y)∂z∂x=?

Q: xlet X,Y,7 be v.V.J with Joint fA くれく くらくtyerzc

A: The joint probability density function is given to us the conditions on x, y, z are also given to…

Q: f (x, y, 2) = x³ /+42³y² – xyz +x² – Vz5 VI+ 42°y? – ryz+ x² – Vz5 - -

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Q: O eiz dz < z2 – i e2 , 3 - z(t) = 2e", t e [0,27]. true False

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Q: ='i+(2xz - y)j XZ and (2, 1, 3) is

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Q: Determine Df(4, -1,6) for f(x, y,z) = ery +4zx in the direction of (-3,2,6).

A: