6. Consider the system: | | dt = 2.r y(8 + 2y) + 2ry

Q: find extreme Value of function fex, y) = x°t 3xy?-3x²-3y=t7 1

A: Given:  fx,y=x3+3xy2-3x2-3y2+7 ⇒fx=3x2+3y2-6x, fy=6xy-6y To find extreme points put fy=0, fx=0…

Q: e. domain: [-3, 1)U(1,3]; range: [-2,4) 8. Let f (x) =x² . Find and simplify the indicate %3D 2. fy…

A:

Q: Eliminate the constant: 3x 3x y=c₁₂e³+€₁₂€ ³ Oy"-4y+3y=0 Oy"-6y¹+9y=x Oy"+ 6y' +9y=0 Oy"-6y'+9y=0

A: Given: From the above, we see that the root of the characteristic equation will be 3, 3. So, the…

Q: Solve for the orthogonal traysctories x*(3k-x) - ky². = x ? 2

A:

Q: ?w Əv у Find when u = 0, v=0 if w=x² + ₁ x=6u-2v + 1₁ y=u+4v - 1.

A:

Q: Obtain the Selution of diffnential equation Sec Y x2-4x +5

A:

Q: dy if y= 3x Find dx х2+1 3(1-х2) D) (x2+1)2 3x2-3 A) 3. 3 B) 2x C) (x2+ 1)2 х2 +1

A:

Q: & lve by line x=+I and line y I

A: The integration of [(x2+xy)dx + (x2+y2)dy].

Q: Evaluate x² + 1 – Vx²2 – 1 dx - Va4 – 1 |

A:

Q: -t,x-1 dt

A: Please see the explanation below

Q: The lines y where = and y = MON 5x - 7 and y = 2x + 8 intersect at the point (x, y) N

A: To find the intersection of given lines.

Q: Differentiate in two ways: y = (x + ¹)(x - ² + 1)

A: We know that the product rules of the derivative d/dx(uv)=u*(dv)/(dx)+v*(du)/(dx)

Q: +タ x2 – 1

A:

Q: Find mZX (3y-71° X Y (2x) O W (x+181° (3y + 1)º

A: Solve for the angle X

Q: Find f.(x, y) and f,(x, y) for f(x, y) 3x3 + 8y? – 6x + 4y and evaluate each at f(4, 5). f.(x, y) =…

A:

Q: Determine if F = x²yî + (xyz +29)ĵ – x²y²k is conservative or not %3D

A: For vector field F⇀=ui^+vj^+wk^ Curl(F)=i^j^k^∂∂x∂∂y∂∂zuvw   For vector field F⇀ to be conservative…

Q: Find: U(x1, x2) = 2X1X2 O X1X2 2x1 2 2x2

A:

Q: Q1: If w-f(z)=z'-z²+2z+2 find u and y and calculate the value of f at z-1-21. V.

A:

Q: What are the points of inter section of y = 8 and f(x)

A:

Q: Q4) Find the linearization of: f(x) = x³ + 10 when a = -3

A: l(x)=f(a)+f'(a)

Q: 2. In y = c+ C2*

A: We have to eliminate the arbitrary constants c1 and c2 from the equation lny=c1+c2x. This is…

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

A:

Q: Vxdx 2. For J T-Vx use 4 O u = JA u = x O u = Ja

A:

Q: find the derivative of (2³ + j)² O 23 +j O 223 + j O 625 + j6z² O 325 + j3z?

A: Derivative of (z3+j)2 is 2(z3+j)2-1(3z2+0) = 2(z3+j)×3z2 = 6z2(z3+j) = 6z5+j6z2

Q: 2 Ⓒz² = x² + y² 2

A:

Q: The change of the energy efficiency function ( P ) of a factory with respect to uj and u2

A: In this question, we have to find the maximum value for the two-variable function. Here we use the…

Q: Q: (2x+y)(x+y) ах Find -?

A: Given query is to find indicated partial derivative.

Q: the doi n ain of the functions

A: We have given two functions : f(x,y)=1xy…

Q: 2 f: TR² x R² → R f (x, y) = 1 (2ax₁ y₁ + bx₁ y₂ + bx₂y₁ +2Cx₂4₂) 2 Examine whether the function is…

A: Given :   fx , y =122ax1y1 + bx1y2 + bx2y1+2cx2y2 To check : whether  f(x ,y) is 2 - linear  and…