Find the values of the constants a, b, c so that F = (axy + bz*)i+ (3x² – cz)j + (3xz? – y)k Is irrotational.

Q: Let f(z) = 5z2 + 4z. Find u(x,y) if z = 8.17 + 3.6i. %3D Round off your final answer in five decimal…

A: Please find the attachment for the details solution

Q: (B) Find the solution of f(z) = x'+6x'y+i 3x'y by using Cauchy-Riemann method

A: we have to solve the given problem

Q: S = In sec 3x| + C 13. z sec² 3x dz %3D 3 - tag 3z,- å

A:

Q: 3. If V =(3x'y-z,xz' + y",-2r?:'). Find grad div at the points (2,-1,0).

A: Given , V=< 3x2y-z, xz3+y4, -2x3z2 > To Find , grad divV  Let  V=< V1 ,V2 ,V3 > On…

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

A:

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: 6) If F = (3x²y – z)i+ xz3 + y*)j – 2x³z²k, find V(V - F) at the point (2,1,0).

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 y = e3x and y = e-3x , prove that: - %3D d²y 9y = 0 dx2

A: Given: y=e3x⇒dydx=ddxe3x⇒dydx=3e3xNow,d2ydx2=ddxdydx       =ddx3e3x       =3ddxe3x       =33e3x…

Q: The local linear approximation of (1- x)2° at x, = 0 is a) 20 - x c) 20 +x b) 1- 20x d) 1+ 20x

A: As per the company guidelines we can solve first question. I hope that the given solution will help…

Q: 3. Eliminate the arbitrary constants c, and c, from y =c, +C,e* y" - y +x = 0 c. y" - 3y' = 0 a. b.…

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: Eliminate the Arbitrary Constant(s): 1. y = c,x2 + C2xe* 2. Iny = c, + C2x

A:

Q: Compute the discriminant D(x, y) of the function. S(x, y) = x' + y* – 6x – 2y + 1

A:

Q: Find the general/particular solution of the follow 1. xy' - y = 2x Inx 2. (1+ x)y' +y = vx 3. t+2y =…

A: The general solution of the differential equations

Q: b) By using the given substitutions, show that i. Sx(x – 3)5dx =÷(x- 3)“(2x + 1) + C, z = x - 3 14…

A:

Q: Find f, and f, for f(x,y)=y In (2x+7y).

A: F(x,y) = y ln(2x + 7y) To find : fx and fy

Q: Q1 but f(x,y) = x²y²sin-'O xf, + yfy = 4f (x,y) between

A:

Q: Given f(x,y,z) = x³yz². Find fy(1,1,1)

A:

Q: Use the method of integrating factor to solve the linear ODE y' – 3y = 1-e-2".

A: Given: y'−3y=1−e−2x

Q: f[x'+zy2,y²2x2], then prove that [y?-zx] (a?-yz] dy [z-xy] du -o. If

A:

Q: By making the change of variables u = 2, v = x, find the general solution of yfyy +fyx + fy = 1.

A:

Q: 2d) Let a e R find the solution of y' (x) – ay(x) = 0

A: as you didn't mention question number to be solvedso I solved first question. For Further solution…

Q: Determine the orthogonal trajectories for x2 = ky³. A) 2x2 + 3y2 = c C) 2x2 – 3y? = C - D1.2

A:

Q: Find the solution of the PDE t> 0, x = [0, π] x= [0, π] √u₁-ux = U₂ [u(x,0) = 3 senx + sen3x,

A:

Q: Given f(æ, y, z) = 6x² + 3y² + 4z², find f-(x, y, z) = | fy(x, y, 2) = | f:(x, y, z) =

A:

Q: lf f(z, y) = 5ery + 1 sín (inr + y) + 2r + 3y, find-a-,-,-and

A:

Q: Q: If u =f(x² +2yz, y² + 2=x)Prove that (y-ax

A: Step by step compute the derivative with respect to each variable x,y or z. Then substitute it in…

Q: Let f(z) = az4 + kz3 + bz2.  Find u(x,y) if z = 6.2 + 2.4i , a = 6, b = 18, and k = 3. Round off…

A:

Q: Q3: 1f f(x, y) = 4xCy5 + 6x*y* .Prove that: f(x,y) * fxxyy fxx * fyy = 1

A:

Q: 2. In each exercise, obtain the particular of solution. 2y-) dy = 0: when x= 0, y = 1 (3x +v) dy =…

A: As per Bartleby guidelines for more than one question asked only one is to be answered please upload…

Q: Exl Let c R,Z) be usual toP s Pace and A-fcxy)ER/ x²+y²< 13 find A Ext CA), Ā , A°

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: Find f,, fy, and f, for f(x,y,z)= 5xy+ 3xz + yz.

A: It is partial derivative

Q: Find those constants a, b, c, d such that f(z) = ax² + bxy + y² + i(x² + cxy + dy?)

A: The given function is : fz=ax2+bxy+y2+i(x2+cxy+dy2)

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: The function U(x, y) satisfies the equation a²U_a?U + ax2 ' ay2 = -2, at every point inside the…

A:

Q: b) u(х, у) on the domain 0 < [z| < ∞. x² + y? Why is v(x, y) single-valued in b?

A:

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

A:

Q: Given f(x, y, z) = x³yz². Find fy(1,1, 1).

A:

Q: x²y" – 4xy'+6y= 0, y(2)= 0, y'(2)= 4 %3D -

A: Given differential equation is: x2y''-4xy'+6y=0           y(2)=0; y'(2)=4 In Cauchy Euler method we…

Q: Is F(x,y)= (2²y,5– zy²) source free?

A:

Q: 2R then the constants R TCX If f(x) Rsin .2 S,f' and f(x)dx and S are respectively.

A: Introduction :Here we have asked to find the value of R and S

Q: Solve the second-order DE y"+2y'+4y= g(1), y(0)= 0, y'(0)=1, where 2, Ost<2 g(1) ={-2, 2si<4 0, 124.

A:

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

A:

Q: Find the orthogonal trajectories of x2 + y? – 2cy = 0

A:

Q: Find f (1, 1) S(x, y) = In( %3D Vx² + y²

A:

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.