dw Find ду and ду at the point (w, x, y, z) = ( – 4, – 2,1,2) if w= 2x?y? + 2yz - 2z3 and x2 + y? + z? = 9. X %3D ду X (Simplify your answer.) ду (Simplify your answer.)

Q: v²u = 0, 0 < r < a, 0< z<l и (r, о) 3D f (r) и (г,1) %3 9 (г) и (а, г) %3 0

A: Given that ∇2u=0u(r,0)=f(r)u(r,l)=g(r)u(a,z)=0 Take u=R(r)Z(z) Substitute in the equation,…

Q: f(x, y, z) = 4xy-8xyz + 7yz2 %3D (x, y, 2) = %3D x, y. 2) = %3D x, Y, 2) = %3D

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Q: y' – mzy = Cem* where C,m, mzare constant and m, # m2 a. y = em1* + C2e™2* b.y = Czem* + Cze™z* c.y…

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Q: = (5, 2) and w = (4, -3), write v = (17,-7) as a linear combination of u and w if sible. Show your…

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Q: Find (2) and (7) at the point (w, x, y, z) = (48,1, -2,-2) if w=3x²y² + 3yz - 3z³ and x² + y² + z² =…

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Q: (x, y) = (0,0) %3| = {r3+y3' 0, (b) f (x, y) (x, y) # (0,0)

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Q: 5. (2D² + D² – 3D)y = 0 -3x a. y = C, + Cze¯+Ce¬* 3x b.y = C, + Cze + C,e* c.y = C, + C;e+ C,e* d.…

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Q: 4 x +y] c) Find x, y, z, t where 3 + 2t 3

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Q: f(x,y,z) = 2x + y? - z2, g(x, y, z) = x - 2y = 0 and h(x, y, z) = x + z = 0. %3D

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Q: 50 W 30 N 40 50 30 20 40 25 60 Part A: AS = Part B: WE = Part C: EN = Part D: AR + RS - AS %3D

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Q: Simpliny O) 5a + 3a %3D

A: Given: a) 5a  +3a b)7b  -5bc)5a-3a

Q: 5 Jlgu ntinuity equation satisfied by u= 3x^2-2y^2, v=-6xy IO 4xy+y?, v= 6xy+ 3y .II O U = u=x-4y,…

A: We have to solve given problem:

Q: // | *dædydzB = {(x, y, 2) =€ R® 0 <« < 1,0 < y < 1,0 < z < x} {(x, y, 2) =€ R° 0<æ < 1,0 < y < 1,0…

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Q: dw Find ди dw, and if w = x3 + In (=) + y, x = u? –+ 5 and v = - dv v y = 3v + 5u and point…

A: Given w=x3+lnxy+y, x=u2-uv+5 and y=3u+5v. Find ∂w∂u and ∂w∂v.

Q: 3y + ne first octant. ) If F(x, y,z) = (5x – y + az)î + (bx + 2y + 5z)j+ (2x + cy – z)k is…

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Q: 45. In AXYZ, W is between Y and Z. The coordinates are X(2,3), Y(5,0), Z(0,0) and W (2,0). What is…

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Q: 2: find fx, fy, and f2. a f(x, y, z) = 1 + xy? - 2z? 5 f(x, y, z) = x - Vy2 + z² c) f(x, y, z) = e 2

A: partial derivative

Q: Q3: If z = f(u,v,t) = Z 3u? + v2 ,u = tet , v= te-2t Then dz at (2,2,0) at

A: Topic:- partial derivatives

Q: 1 Find Vf(P) and Df(P). (a) f(r,y, z) = y² + 2² – 4x2; U = i – +; P(-2,1,3) %3D |

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Q: p = z, 39 = zy a 2y(z- 3)p+ (2x- z)q = y(2x- 3) %3D 1

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Q: xa, + ya, + za, Let A show that V XA = 0. %3D (x² + y² +

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Q: Find the values of w, x, y, z and Dx x + y + z + w = 13 2x + 3y - w = -1 -3x + 4y + z + 2w = 10…

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Q: B. Let Y = {a, b,c} and Z = {1,2} %3D %3D 1. Find Y x Z

A: Given: Y=a,b,c and Z=1,2 To find:  (1) Y×Z (2) Z×Y (3) Y×Y

Q: Q5: Find Zyx if Z = f(u, v) , u = xy and v = X + y. %3D

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Q: xa, ya, + za Let A = (x² + y? + )3/2 i show that V X A = 0.

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Q: التكن كل من R.Q علاقة معرفة كالاتي R={(x,y)|(x,y) EN*N|x +y= 5} Q={(X,Y)|(x.v) EN*N[ 2x - y= 4} RUQ,…

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Q: II. (²z + y²z) ds S is the hemisphere x2 + y? + z² = 9, z

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Q: Find (ay), and (3x), ду ду X Əw = dv X (Simplify your answer.) at the point (w, x, y, z)=(1,-1,1,…

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Q: dw Find and using the chain rule. ди 3 w(x, y, z) = x = u² + v², y = u² + v², z = 2uv. %3D x² + y? +…

A: The solution is given as

Q: find ƒx , ƒy , and ƒz . ƒ(x, y, z) = e-xyz

A: Given fx,y,z=e-xyz Partial derivative means differentiating with respect to one variable keeoing…

Q: Find f, (x,y) and f,(x,y). Then, find f, (2,1) and f,(- 2,4). f(x,y) = In |3+: 2x?y³| ..... 1, (x.y)…

A: Solving the problem by doing the partial derivative of the function.

Q: Find Vf at the given point. 3 f(x,y,z) = x³ + y² − 4z² + z lnx, (1,5,3) Vf|(1,5,3)+(+()k (Simplify…

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Q: f(x, y) %3D 3ху + у? (а) f(x + Дх, у) f(x, у + Ду) — f(x, у) - (b) Ду Зх + 2y + Ду Ду # 0

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Q: aL d( aL (i = 1,2, ,n) ... aq, dt dg,

A: We have to prove given result:

Q: 5. (w3 + wz² – z)dw + (z³ + w²z – w)dz = 0,when w = 4, z = 2 %3D %3D

A: The differential equation can be solved by separating the variables on each side and integrating…

Q: dw ду Find OW at the point (w, x, y, z) = (9,3,1,1) if w = x²y² + yz - z³ and x² + y² + z² = 11. dy…

A: Given: w=x2y2+yz-z3x2+y2+z2=11 The objective is to find the partial derivative of w with respect to…

Q: Find the order of the given DE. Also, decide if the DE is linear or nonlinear. (a) + yx = x (b) 1-…

A: The differential equation dydx+y2x=x contains the highest derivativedydx which is of first order.…

Q: Evaluate ∭B ze x+y dV where B is the box determined by 0≤x≤5, 0≤y≤1, and 0≤z≤4 The value is

A: the integral given to us is  ∬∫Bzex+ydV                (1) where B is s the box determined by 0≤x≤5,…

Q: h = -3, k = -2 and r = 7 %3D (x - h)? + (y - k)? = r2 ww x2 + y2 +Dx +Ey + F =

A: We have to solve the equation

Q: Evaluate (D5 – 5D4 + 7D3 + D² – 8D + 4)y = 0 a. y = (C1 + C2x)e¬* + (C3 + C4)e¯ b.y = (C1 + C2x)e* +…

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Q: a) a = 0,10, dfy = 8, dfp = 10. Fg = %3D %3D b) a = 0.10, dfy = 8, dfp = 6. Fo = %3D %3D c)a = 0.10,…

A: Here critical values from F distribution table

Q: dw dw Find ду at the point (w, x, y, z) = (4, – 1,1,1) if w = 4x²y² + 4yz – 4z3 and x? + y? +z? =…

A: The given equations are w=4x2y2+4yz-4z3 and x2+y2+z2=3 at the point w,x,y,z=4,-1,1,1. Find the…

Q: Find f(x,y) and fy(x,y). Then find fx (2, -1) and fy (-4,3). f(x,y) = In 5x4 +8x²y²| fx(x,y)=…

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Q: 3x d.A, A= {(x; y) E R² : y E [0, 1], x € [y, e®]} .

A: Given: A double integral ∬A3xdA, A=x;y∈R2:y∈0,1, x∈y,ey ∬A3xdA=∫01∫yey3x dxdy=3∫01x22…

Q: f(x,y)=21 (x+y), x=1,2,3, ; y=1,2 0 , d.d.

A: Given :- fx,y = 121(x+y)        x=1,2,3 and y=1,2 we have to calculate cov(x,y)     Formula:- Covx,y…

Q: y" = 4(y-x), 0 sxs1, y(0) = 0, y(1) = 2, %3D

A: To check: given 2(a)  has unique solution.

Q: +y f(z, v) = "" I> 0, y > 0, 3- 3y > r. %3D

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Q: Ion 41 Let A = (m, n) and B = (x, y). If A and B lie in on horizontal line and B is to the right of…

A: We will solve the problem using figure.

Q: f(x, y, z) = 4x²y - 8xyz + 10yz? (x, y, z) = %3D x. Y. z) = f,(x, y, z) =

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Coordinate Geometry

Coordinate geometry, also known as analytic geometry or Cartesian geometry in classical mathematics, is a type of geometry that is studied using a coordinate system. Coordinate geometry is a branch of mathematics that describes the position of points on a plane using an ordered pair of numbers called coordinates.