find the domain of the given function. f (| x , у) %3D Vx²-2y .A D= { (x, y) ER?: ys x } 2 .B D = {(x,y) ER?: y < 2x?} .C 1 D = {(x,y) ER?: y 2 x?} .D 1 D= { (x,y) ER?: y s x²} 글

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: I) Consider the function: y = + C,e2x + C,e-5x + Czxe-5x

A:

Q: Find the largest domain (in R²) for the function 1+ Vx + /y x2 + y2 f (x, y) :

A: Given that, fx,y=1+x+yx2+y2 To determine, the largest domain in ℝ2 for fx,y

Q: nd the absolute maximum and minimum of the function f F(x,y) = yx² where - 2<x<2 , -1<y<1

A:

Q: For which value of k is the function x+y? f(x, y) = { 2-Vx² +y² +4 , (x,y)#(0,0) k (x,y)= (0,0)…

A:

Q: find the specific function values. ƒ(x, y) = x2 + xy6 ƒ(-3, -2)

A: Given function:

Q: Find the point of diminishing returns (x,y) for the function R(x), where R(x) represents revenue (in…

A: Given: R(x)=10000-x3+45x2+700x, 0≤x≤20

Q: Examine the function f(x, y) = −3x² - 4y² + 15x - 8y + 5 for relative extrema.

A:

Q: Joshua wants to find the local maxium and minima of the two variable function F(x, y) = x³ +y² – 48…

A: We will find out the required points.

Q: find the domain of the given function. Vx²-2y ,2. f ( x, y ) : .A D= {(x,y) ER?: y s 2x²} .B D= {…

A: Option (B) is correct

Q: The function f(x, y) = -3y + 2√√ry is a

A:

Q: Find an equation for the level curve of the function f(x,y) that passes through the given point.…

A:

Q: find the specific function values. ƒ(x, y) = x2 + xy5 ƒ(2, 3)

A:

Q: Find the domain of the function f(x,y)= exy/ x-y2

A: Answer-

Q: Suppose that f(x, y) = e² / y on the domain D = {(x, y) | 0 < y < 2,0 < x < y³}. D

A:

Q: Examine the function f(x, y) =-3x-4y+15x - 16y + 6 for relative extrema.

A: Here we have to find relative maximum.  The solution is in both 1st and second steps.

Q: 2. Match the functions with its graph. y = Vx – 3 b. y = 3 vã c. y = v – 3 d. y = v-x+ 3

A: Part a,Given,         The function is y=x-3.

Q: Q3/ Optimize the function Z = x + x ? Subject to: x1 + x2 4 x1, x2, 2 0 Using Lagrange multipliers.

A:

Q: Consider the utility of a consumer consuming two goods, the quantities of which are x and y. His…

A:

Q: Does the given equation F(y, r) = r – 2x?y + 3ry 22 = 0 define an implicit function around the point…

A:

Q: Find the point of diminishing returns (x,y) for the function R(x), where R(x) represents revenue (in…

A: Point of diminishing return is the point where the marginal return starts to diminish. Point of…

Q: df f(x) = x² + 4x – 5, x > – 2, find dy For the function y = y=11 (f-1)'(11) = Preview

A: Subtract y. Then try to solve for x using quadratic formula.

Q: Find the point of diminishing returns (x,y) for the function R(x), where R(x) represents revenue (in…

A:

Q: find the domain of the given function. f ( x , y ) = Vx²-2y .A D = {(x.y) ER?: y 2x²} .B D= {(x, y)…

A: We find domain of given function

Q: find the specific function values. ƒ(x, y) = x2 + xy4 ƒ(-1, 1)

A: Given: fx,y=x2+xy4, f-1,1 for finding given value we substitute x=-1, y=1 in given expression

Q: The function z = f(x, y) = 2x + xy – y? %3D %3D - is given, where x = g(y) = 3y? %3D

A:

Q: Find the critical local extreme points (if any) to the function -2x3 f(x, y) = + y? + 8x — 6у 3 Vour…

A: We will find out the required critical local extreme point.

Q: Find the largest domain (in R²) for the function 1+ Vr+ Vỹ x² + y² f(x, y) : =

A: Given: The function f(x, y)=1+x+yx2+y2.

Q: For the function f(x,y,z) = 3 + xy5 - 5z4, find fx , fy , and fz.

A:

Q: For what values of  r does the function satisfy the y =  e rxequation  y"  + 6 y'   + 8y  =0?

A: Given function y=erx To find value of r which satisfy the equation y"+6y'+8y=0 Solution:…

Q: Find the relative maximum and minimum values. Зx2 f(x,y) = + 10y2 + 3

A:

Q: find the domain of the given function. x²-2y f ( x, y ) = .A D = {(x.y) €R²: y 2 x²} .B D= {(x,y)…

A: Given function is  f(x,y)=√(x^2 - 2y)

Q: df For the function y = f(x) = x² – 3x – 3, x > 1.5, find dy y=12 (f-1)'(12) =

A: Given  y=fx=x2-3x-3; x≥1.5

Q: The function f(x, y) : 1+2? +y? is 1-x2 -y? discontinuous at the points {(x, y)\æ² + y² # 1}. True…

A: The given function is f(x,y)=1+x2+y21-x2-y2

Q: Q5: Find the max and min points for the function: F(x,y) = x2+xy2-4x+1

A:

Q: Consider the function f(x, y) = x² – 6x + y? –- 2y + 10. Sketch the domain of the function h defined…

A:

Q: Find the optimal values ​​of the function f (x, y) = 4xy + 5. Subject to the restriction x ^ 2 + y ^…

A: Consider the objective function as fx,y=4xy+5 subjected to restriction equation x2+y2=18. Let the…

Q: Sketch the level curve of the function V(x, y) x² + y? for c 64. %3D

A:

Q: Find the extrema of f(x,y) = -2x² + y taken on the graph of x + y? = 0.

A:

Q: find the specific function values ƒ(x, y) = x2 + xy3 a. ƒ(0, 0) b. ƒ(2, 3)

A:

Q: Calculate (a) r(4)F(3/4)/r(7/4) , (b) Factorial function x"e*dx = n!

A: Here, Definition of Gamma function is ∫0∞e-ttx-1 dt= Gamma(x).

Q: Sketch the level curve of the function f(x, y) = x² + y? 2 for c = 1.

A: Level curve:  The level curves of a function f of two variables are the curves with equations f (x,…

Q: The function y = x³ + ax? + bx + c has a stationary point at (-3,12) and it passes through the point…

A: Since, the function y=x3+ax2+bx+c passes through the point (0,2)⇒2=0+0+0+c⇒c=2-(i)Also, we have been…

Q: Determine the extrema of the implicit functions: (2² + y² + z²)² = 1 – a² – 2², z = 2(x, y) | |

A: Given x2+y2+z22=1-x2-z2 Differentiate with respect to x:…

Q: The domain of the function f(x, y) = 3x + xy + 5y? is R.

A: We have to verify that the domain of the function fx,y=3x+xy+5y2 is R or not.

Q: y? For function f (x, y) x2+1 Starting from the point (1, 2), at which direction does the above…

A:

Q: Q4) f(x, y) = x'/3 – x/ay² is harmonic ? Does the function

A: our objective is to conclude result.

Q: A company that produces skis has the Cobb-Douglas production function Q=f(x,y)=180x0.7y0.3 , where Q…

A: The product function is given by, Q=fx,y=180x0.7y0.3 Here  Q is the number of pairs of skis…

Q: (b) Find the Linearization of the function: f(x)= Vx at a= 27 and use it to approximate the number…

A: Let the function is f(x)=x3 Let a = 27   Formula: Linearization of the function f(x) at x = 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.