(a) F(x, y, z) = i + 27 + 3K. (b) F(r, y, 2) = i+ 25 + zk. (c) F(r, y, z) = xi+ yj+ 3K. (d) F(r, y, 2) = ri + y3+ zk. II :0 2 0- III IV 2 0- -1- 10-

Q: (xy(x²-y²) Let f(x, y) =} (x²+y²) (x, y) ± (0,0)| show that fxy (0,0) + f yx(0,0) (x, y) = (0,0)

A: This question is taken from the partial derivative in which we have to prove the given statement. We…

Q: f(x, y, z) = x – Vy² + z

A: Take the partial derivative ony by one with respect to x, y & z considering other as constant at…

Q: Find ∂ w/∂ x at the point (x, y, z) = (2, -1, 1) if w = x2 + y2 + z2, z3 - xy + yz + y3 = 1, and x…

A:

Q: f(x, y) = /2x – y /2х — у f(x, y) = In(9 – x² – 9y²) f(x, y) = /1 – x²? - VI – y² S(x, y) = Vy + /25…

A:

Q: Find ∇2f, given that f(x, y, z) = 1 / (x2 + y2 + z2)1/2.

A:

Q: f(x,y) = 3x-x- 2y ty faa(ay)= -6x fyy (3,9)= 123°-4 D(x.y) = faafyy-[tay]²- - 72ny² +24% ニ 12ay2+ こ…

A:

Q: f(x, y, z) = 3x²y - 5xyz + 7yz2 2. f,(x, y, z) = f,xx, y, z) = f(x, y, z) =

A: Given query is to find the partial derivative for the given function f(x,y,z).

Q: 1 If f(x, y,z)= ôf then 2у - х —z a. 2 (2y-x-2) b. 1 (2y -x-2)2 с. -1 (2y –x-2) d. 1 (2y–x-2)

A: It is derivative problem.

Q: f(x,y) = 6x +3y %3D V f(æ, y) = %3D 3.5 f(x, y) = 6x°y³ Vf(x, y) = f(x, y, z) = 6x+3y5+ 825 V f(x,…

A: SOLUTION-

Q: Vx? + yZ 49x2 49 [F,(x, y)]² + [f,(x, y)]² 1+ x² + y2 e have [f,(x, y)]² + [f,(x, y)]² = /

A: This is the question from vector calculus.

Q: Determine whether X and Y are independent: 2e--2y x, y > 0 a. fxy(x, y) =

A: Hello! As you have posted 2 different questions, we are answering the first question (4-2). In case…

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…

A:

Q: 16 -Σ(Σ») f(x, y, z) = Σ · (x + y + zn?) 2

A: Given: fx,y,z = ∑n=116∑k=1nk-x+yn+zn22

Q: 2. If F(x, y, z) = 2z3 – 3(x² + y²)z, then verify that Frx + Fyy + F2 = 0. %3D

A:

Q: Suppose that f(z, y) = 10z²y² + 8z? + 2y? then find the discriminant of f.

A: We have to find the discriminant of the function of two variables fx, y. It is given that the…

Q: If V = (3x + 2z²)i + j- (z – 7x)k then V. V at the point. (1, 1, 1) is ||

A:

Q: (a) f :Z → Z, where f(x) = x². g : Z → Z, where g(x) = |æ|². %3D (b) f :Z × Z → Z, where f(x, y) =…

A:

Q: f(x,y) = x² + 3xy +y² fonksiyonu için fex (2,3)]. [fyy (2,3)] – Fzy (2,3)]? =

A: The answer is, (-5) The detailed solution is as follows below :

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: af Given f(x, y) = In(3x² + 5y²) then || 3T 3z2+5y 10y 322+5y? 5y 3z 45y 6z %3D

A: Let f(x, y)=ln(3x2+5y2) Differentiate f(x, y) with respect to x ∂f∂x=∂∂xln(3x2+5y2)

Q: 2. W =I+xy- Z finds Wzz WZX NJ 3.

A: Given W = 1 + xy2 - z2

Q: af (2,0) ay f(x, y) 3D хетУ + 5у%; af (2, 0) = Əy

A:

Q: If F(x,y,z)=x?y-y²z3 Then fz= -3y²z2

A: Given: fx, y, z=x2y3-y2z3

Q: Find Duf at P. 2, -k 3' 2 f (x, y, z) = 6x³y°z°; P(2, – 2, 2); u = i+ 3 -

A:

Q: f (z,y, z) = x² + y² + 2² subject to zyz = 4

A: Given: fx,y,z=x2+y2+z2 subject to xyz=4 Let gx,y,z=xyz-4 Using Lagrange Multiplier fx=λgx, fy=λgy,…

Q: f(x, y, z) = 3x + 2y + 4z, x2 + 2y2 + 6z2 = 21

A:

Q: 7. f(x) = x² In x, f"'(x) 1 8. y = -, y" 1 .f"(q) 9. f(q) = 2g* 10. f(x) = /x, f"(x) 11. f(r) = /9 –…

A: The objective of the question is determine the derivative of the given function "y".

Q: (x, y)Rz + z = x V z = y (x, y)Sz → (x – y²)² + (z² – æ²)² = 0

A: Given: x,yRz⇔z=xVz=yx,ySz⇔x-y22+z2-x22=0

Q: Let f(x, y, z)= = fz(x, y, z)= fy(x, y, z)= fz(x, y, z)= 2² - 2y² I y² + 4z² Then

A:

Q: The antiderivative of the function f(r) = 2.5 .0+7.3z is %3D -2.5 + 1.8z +c -2.5 0+1.8z+ c 6. -2.5…

A: We will integrate the function and use c as the constant of integration.

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

A:

Q: Prove if X,Z, y > 0 xy (3x +2y – 4z)+ yz(y+3z – 4x)+ xz(x+2z –- 4y)>0 then

A:

Q: x² + y² = (2x² + 2y² – x)', (0,¿), (cardioid) -

A:

Q: f(z) = 4z² – 2z + 9 إجابتك = Vx %3D f (z) = 4z² – 2z + 9 إجابتك

A:

Q: [2xy + yz (i) F(x,y, z) = x2 + xz with domain R³. || xY

A: “Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: ∇⋅F of F = (2x3y)i-(3y2z)j+(xz3)k at (1,2,-1). a. 27 b. -34 c. 4 d. -7

A: The del operator is used to represent the partial derivatives with respect to the variables defined…

Q: Display the values of the functions in Exercises 37–48 in two ways:(a) by sketching the surface z =…

A:

Q: e-", if 0 3,

A:

Q: 3. Find and at (0,0) where if (r, y) # (0,0) if (z, y) = (0,0) f(1, y) = Are they equal?

A:

Q: (a) F(r, y, 2) = 7+ 27 + 3K. (b) F(r, y, 2) = i + 25 + zk. (c) F(r, y, z) = xỉ+ yj+ 3K. (d) F(r, y,…

A:

Q: ( a) 2.xdV where E = {(x, y,z) |0 < y < 2, 0 <xs/4- y² ,0 < z< y } E

A: As per Bartleby's answering guidelines, we are supposed to answer one question if more than one has…

Q: əz əz +y show that x 3z x²y2 B. If z əx ду %| x+y’

A: B). From the given function: z=x2y2x+y And x∂z∂x+y∂z∂y=3z As we know that the Quotient rule:…

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

A:

Q: f(x, y, z) = 4x²y - 2xyz + 9yz2 (X, y, z) = ,(x, y, z) = f_(x, y, z) =

A: Answer and explanations is given below...

Q: f(x) = 2x5 + 15x4 - 3x3-4x2+ 7x+ 14 1)Trapeaoidal rule 2) Trape20idal rule with n=2 3) 1/3 Simpson…

A:

Q: 2xy F(x, Y) =Vx+ 2y (1, 1) f,(x, y) = 1,(1, 1) S(1, 1)

A:

Q: z = f(x, y) = r* – x²y+ 4y, r= g1(u, v) = u² + v², y = 92(u, v) = = uv.

A: Let's find.

Q: 2. f(x, y, z) = exyz² Find fxyz

A: