6. Find the domain of y = Vx+ 4x + 5x + 2 + Jxl-|x+1]

Q: 3. Let f(r, y) = y²x – yx² + xy. Find all critical points of f.

A: We have to determine critical points of f

Q: 3. Find the fixed point(s) of f : [1, 0) → [2, 0) defined by f(x) = vx² + x.

A:

Q: Find the domain and range of:

A: (a) We know that the domain of the square root function is always greater than equal to 0. Thus,…

Q: compute ∫_∂D(x^2ydx+xy^2dy, where D is described by 0≤x≤1, 0≤y≤x

A:

Q: 16. Of all points (x, y, z) that satisfy 3x + 4y + 2z = 52, find the one that minimizes (x – 1)2 +…

A: Let f(x,y,z)=x−12+y−42+z−22   and    g(x,y,z)=3x+4y+2z−52≡0Apply Lagrange Multiplier method to find…

Q: Let f (x, y) = 2x3 + x2y - y2. Compute d2f/dx2, d2f/dy2, and d2f/dxdy at (x, y) = (1, 2).

A:

Q: 2. Evaluate f. (y²dx + x?dy) where C is the triangle with vertices (1, 0), (1, 1), (0, 0).

A:

Q: If y(x) satisfies y′′(x)=y′(x)(1−y′(x)),y′(0)=1/3,y(0)=1, then y(x)=?

A:

Q: If u =f(x² +2yz, y² + 2zx ).Prove that (v² – zx) + (x² - yz) ди + ди ху

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: 1. Let f(x, y) = x³y+ 12x² – 8y. Find all critical points of f.

A: As per our guidelines we are supposed to answer only one question at a time. So I am solving the…

Q: Z=8x+12y subject to 4x+6y>14 , 4x+5y > 9, x20, y20 x=? (2 decimal places) Minimize

A:

Q: 8. Find and classify all the critical points of f(x, y) = 4x²y+2xy² - 6xry.

A:

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

A:

Q: 4,5 f (x,V)= Sx"y%,compute fx and fy

A:

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: f(x, y) = In (x²y - x) %3D

A: Here, the given function is: f(x,y)=ln(x2y-x) First to find the first derivatives:…

Q: Find the particular soluti y' + 3x²y = 3x² %3D Initial Condition: y = 6 %3D

A:

Q: Let f (x,y) =In Then f „(1, – 1) =... 3x²+ 4y3

A: This is a problem of partial.

Q: (8) If w = 5x2 + 2y2, x -3s +t, and y s - 4t. %3D aw and at aw Find as

A: w=5x2+2y2,   x=-3s+t,  y=s-4t

Q: of of and ду Find f(x,y) = Vx + 3y?

A:

Q: 2. Show that the function u = p(xy) + Vry ý(y/x) provides the equation n, = 0. dy? U -

A:

Q: 4) Suppose that T : R³ → R² is defined by T((x, y, z)) = (1+2x – z , 3 – x + 6y) Is T linear?…

A:

Q: 6) If y=x² +1+ f dt , prove that y"= 2 - x2

A:

Q: 7. Let f(x, y) = 10x³y* + 21xy². Find fyyy. .3,4

A:

Q: (b) If z =W, show that: x- y xy 0 =

A:

Q: If x + y + z = 12 & x² + y² + z² = 96 & !.!,!= 36 then value -+-+ -%3D X y of x³ + y3 + z³ is

A:

Q: Identify the transacation of point P x + 3, y + 1). ddf2d92a ddf892d342a ddf892d342a dd1892d342a…

A:

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

A:

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

A:

Q: 7) Let Z.= 3x2 - y² . Find all points at which |VZ| = 6 %3D

A: There is an ellipse,  all points on the ellipse are the solutions of given equation.

Q: 4 to Use the Trapezoidal Rule with n = 1 approximate J-1 V1-x³

A:

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

A:

Q: ди Ifu=r(x* +2yz,y* +2zx)Prove that (y -zx) +(x² - 3z) + (:* - xy) ZX

A:

Q: Let ulx) be the solution of the IuP xy'-2y:x, yQ)=0 Evaluate y(32) %3D

A: In the question we have to find y(32).

Q: 2. Find and classify all the critical points of f (x,y) = 2x – 9y – xy + x² + 5y².

A:

Q: Prove ¬(3x € X : (Vy ¤ Y : E(x, y))) = \x € X : (‡y ¤ Y : ¬E(x,y)) (Vx X: (³y € Y : E(x, y))) = (3x…

A: We have to prove  a) ¬∃x∈X : ∀y∈Y : Ex, y=∀x∈X : ∃y∈Y : ¬Ex, y b) ¬∀x∈X : ∃y∈Y : Ex, y=∃x∈X : ∀y∈Y :…

Q: 1 3. Let f(x, y, z) = Show that Vx2 + y² + z²° frx + fyy + fz2 = 0.

A: Given fx,y,z=1x2+y2+z2 To show fxx,+fyy+ fzz=0

Q: (ii)If y=(x+Jx* +1. prove that y'= Vx +1

A:

Q: 8. Find and classify all the critical points of f(x, y) = 4x y+ 2xy - 6xy.

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

A:

Q: 2. Let f(x,y) 3x y. If C is the line segment from (1,1) to (2,3), evaluate r'dt.

A:

Q: 2. Given z = , show that ху xy(zxx + Zyy) 2 y - x3 x²y? |

A: Function is the unique relation where each x is mapped to unique y. It can be of many type,…

Q: let 2.+ (3(x-1+4y+!j". ニ ): find the Critical points f f.

A: In the question we have to find critical points.

Q: Find all the relative extremum points and saddle points of f(x, y) = y* – 2y²x – x² + 4x |

A: given functionf(x,y)=y4-2y2x-x2+4x suppose that (x, y)=(a, b) is a critical point of f(x, y)and D(x,…

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…

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

A:

Q: 1- Compute and plot the convolution of y(t) = x(t) * h(t) h(t) = 5e-5t.u(t) and x(t) = u(t) %3D

A:

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.