3) V. (FF) = f (V. F ) + F •V ƒ. 4) V: (F +G) = V. F + v•Ğ. 5) V: (FxG) = Ġ- (V × F ) – F · (V × Ġ)

Q: (b) ruz – 2yuy + u = eª , for x> 0

A: 1.(b) Given partial differential equation xux-2yuy+u=ex, for x>0 This can be written as…

Q: 8) Find the value of x that makes line m || line n. 120 3x E AS

A: “Since you have posted a question with multiple sub-parts, we will solve the first three subparts…

Q: Use Cramer’s Rule to solve…

A: The solution is given as

Q: Find fxy(x,y) if f(x,y) = (x5 +y³) 7. fxy(x,y)=

A: Concept: Partial derivatives: In differential geometry and vector calculus, the partial derivative…

Q: Suppose that f(æ, y) = e" = e-3z? - 4y? +y

A:

Q: if y = secx prove that y^2+y=2y^3

A: Equation relates the number of variables combined together by algebraic entities using equality…

Q: Use Cramer's rule to solve for r' and y in terms of x and y: y = 31' – 2y

A:

Q: 2- find fxx and fyy for f(x, y) = x²sin?y

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: 8z Find at (2, -2, 1) if By z' +y +z2 = 6xz +6yz +21 eej49 1.

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

Q: The line that passes through the points (2,0), (0,1) is x+2y = c, where c = 1. O True False

A:

Q: Find mZR. R 7 mZR %3D Submit

A: Solution: The objective is to find the required angle

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: T: R2 R2 is defined by х + 7х, [3x, – 4x2] X1 %3D and B = {u,,u,} and B' = {v,v,}, where %3D -- --…

A: Given transformation T:R2→R2, defined by Tx1x2=x1+7x23x1-4x2 and B=u1, u2 and B'=v1,v2 Here u1=22,…

Q: for w = ze(zy²+2:). Do not include =" in your answer.

A:

Q: Show that Plx-1,y) = A(x, y) X+ y-1

A:

Q: If x < 0 and y > 0, determine the sign of the realnumber. x/y

A: It is given that, x < 0 and y > 0

Q: af Given f(x, y) = In(7x² + 9y²) then

A:

Q: Find mZG. E 35-/2 F 70/2 mZG %3D Submit

A:

Q: Find fxy(x,y) if f(x,y) = (x5+y³) 7. fxy(x,y) =

A:

Q: Find mZR. 2/2 mZR = %3D Submit

A: From the given figure:   With respect to ∠R   Perpendicular=QPBase=QR=2Hypotenuse=PR=22   From the…

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

A:

Q: Solve Ut = Urx, x > 0, t> 0, u (x, 0) = f (x), u (0, t) = 0.

A: Given partial differential equation isut=uxx,     x>0,     t>0ux, 0=fxu0, t=0

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: If f(x,y,z) = 3zy²e* , grad f =

A: Here we have to find gradient of given function f(x, y, z).

Q: y = v1- x+ x2 ||

A:

Q: the of olution using simplex me Max z = 8x, + 10x, + 7x3 s.t: 4x + 6x3 + 3x3 S 60 7x, + 2xz + 5x, S…

A: In this question, the concept of Linear Programming is applied. Simplex Method An approach to…

Q: II. Verify that ду дх дх ду 3 2 2. f(x, у) %3Dх'у? — ху 'y² – xy ³

A: Given function: Now,

Q: Find fxy(x,y) if ​f(x,y)=(x^3+y^4)^7. fxy (x,y) =

A:

Q: 4. If f(x, y)=: Vx² +y? 1 , find f, and f,.

A: Given data is : fx,y=1x2+y2  To find fx and fy

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: Use Cramer’s rule to solve for x 2x=3y-4z+11 9x+y=z-1 3x-4y=7

A: Given,

Q: D.(1,2), where f(x, y) 14x-y in the directionof v (2,-1)

A:

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: 4) Lett =,u = x? - y² ,v = 4xy³. Find %3D ax ду

A: t=uv

Q: In AXYZ, PQ I| XY.If XZ= 15, YZ= 12, and ZQ = 8, what is ZP?

A: given XZ=15, YZ=12, and ZQ=8What is ZP?

Q: f (x, y) = {* - kx(x — у),0 <x< 2,-х <у<х elsewhere

A: (i) Consider the property for a joint PDF, ∫-∞∞∫-∞∞fx,ydydx=1 Substitute the values,…

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: 11 sec²(3t), 0 < t C₁ and C₂ as arbitrar

A:

Q: If f(x,v) = (y)²x ,Verify fy=fx ху

A: Given:fx,y=y2x Now, the value of fxy will be,fxy=∂2f∂y∂x=∂∂y∂f∂x=∂∂y∂y2x∂x Now, the value of ∂y2x∂x…

Q: Given f(*, y) = 8a'y - 4cy. Compute:

A:

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: Solve Utt - c²uxx = 0, –n 0, %3D и(х, 0) %3D f(x), и(-п,t) %3D0 %3D и(п,t), и,(-п,t) %3D 0 %3Du,…

A:

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

A:

Q: me succe LO SUIVE uie folnoWing 2 и (х)— | (x -t )u (t )dt 2 --

A:

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

A:

Q: 16. Find the points of intersection of x' = 4y and y= 4x. (as:(0,0,(16,64)

A: My Dear student according to the rules of Bartleby we can solve only one question post others as a…