Question 2: Consider U(x, y) = xy. Verify that (1, 1) and (2, 1/2) give the same utility level. Now multiply the two points by 2, that is (2, 2) and (4, 1), and verify if they are still of the same utility level.

Q: Find the maximum and minimum points of the following: 1 1. y = vx- 2. у %3D х3 — Зх2 -

A: Given; 1) y=√x-1/√x 2)y=x3-3x2.

Q: Find the "actual" solution (x,y) for the following problem. max_x2y² subject to 2x + y ≤ 2 x20,y20…

A: Given:    2x+y≤ 2 , x≥0 , y ≥0    Max - x2y2

Q: 1. If g(x) = 3x - 7, find i. g-¹(x), ii. g-¹(8) 5 x+8' 2. If h(x) = i. find h-¹(x), ii. h-¹(3)

A: Given : g(x)=3x-7 and h(x)=5/(x+8)  We have to find inverse of these functions.

Q: If x, y e R satisfy the equation x2+ y2 -4x-2y+5 0 and S (x + ry) then value of is 100

A: Given : x,y∈ℝ satisfies equation x2+y2-4x-2y+5=0 and S=∑r=099x+ry we want to calculate value of S100…

Q: Q2/ Find the domain and range for the following functions 1) y = 2) y = x +! 3) y = 3+2 cDsx 4) y =…

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Q: Determine the location of all extremes and show what type the extremes

A:

Q: For the function f(x,y,z) = 4 + 5xy¹ − 32³, find fx, fy, and f₂. fx=0

A: Given function, f(x,y,z) = 4+5xy4-3z5   To be found - fx, fy, fz

Q: 2. If w = f(x + ct) + g(x- ct) show that c²wxx = Wtt C= constant.

A:

Q: For which values of r is the function y =t" a solution of t?y" – 5ty' + 8y = 0 Select one: O a. r=…

A: Given differential equation is euler-couchy homogeneous differential equation which can be solved by…

Q: 1 Q 2. Differentiate h(x) = (V+ -2 IX

A: The equation can be re written as,

Q: Minimize F = x² +y² with x + 2y = 20. O a. F= 20 O b. F= 72 c. F=2 O d. F= 80 e. F= 60

A:

Q: Consider that there are two goods, good X and good Y, which are perfect substitutes. The consumer…

A:

Q: Number of computer encoders with scores greater than 75 Percentage of computer encoders with scores…

A: Number of computer encoders with scores greater than 75 is = 17+14+4+2+3 = 40 Scores less than 85=…

Q: Faced with two distinct demand functions Q, 16-0.5P, and Q, = 20-0.1P where TC= 100 + 20Q with Q =…

A: Given that: First we have to solve the demand equations for price We get,

Q: Find the following antiderivatvie √8x-5dx A-2x-4 B. COLO 8 -6 5 X C-2x¯*+C D. 8 5 3-6+C

A: Explaination of the answer is as follows

Q: f(x, y) = 8 – + xy. I y

A:

Q: Let f(x, y) = x² – y?. Find (c) The linearization of f at the point (2, –3).

A:

Q: What must be the value of y if u = (1/3, y, -1/2), v = (6, 1/8, 10), and u · v = -5/2. 3 1 4 O 2

A:

Q: 1:Assignment 1. If x²y-xy² + x² + y² = 0 find y 2. If x² - xy + y² = 3 3. If x³y-xy³ = 2 find y' and…

A:

Q: The graph of the function fCX)=x²+dx+q has only one X-intercept Select a valve for d that satifies…

A: For quadratic equation to be only one x-intercept , discriminant should be equal to zero.

Q: Please review and solve the following problem. The screenshot listed already has some work done and…

A: Step 1:Step 2:

Q: Equation xdy + ydx = 0 y"-3y" + 3y + y = 0 (y)¹/² = √/(1+y")4 Order Degree Kind IV DV

A:

Q: 2. Differentiate the following equations. a. Differentiate. 11 y 1=22²2²² 7x²

A: Since we are given with the multiple  number of subpart  question answer will be according to the…

Q: xyy =x +1, with y(1)=2

A:

Q: Find the values of x, y and z that correspond to the critical point of the function f(x, y) = 4x² 5x…

A:

Q: 1. y = V(x2 + 2) – x (x² +2) - х

A: Topic = Derivatives As per guidelines, At a time only one question can be answered out of different…

Q: What value of c will satisfy y(x) = c(1 – x²) given y(0) = 1? 2 O Option 1 Option 2 3 Ontion 3…

A: Let's find.

Q: Match equations y′ ? 1 − x, y′ ? x − 2y, y′ ? x(1 − y) to slope fields. Justify

A: The plot of y'=1-x is as follows,

Q: Use graphical methods to find two solutions to thesystem

A: Graphical method: The point at which graphof two equations intersect is the solution of both the…

Q: Evaluate f(2Vx +=) dx 3 4 X2 ++ c 3 A. - 3. -x2 - x +c 3 4 С. -X2 - 3 D. + 2x5 + c 1/5 B.

A: Integrate normally

Q: Among the values of x for which V(x)=0V(x)=0, which are physically possible?

A: As per previous solution The volume of box

Q: Consider the following problem; max F(x1 ,x2) = x,x3 subject to 6x? + 3x = 72 %3D Find the max…

A: Step:-1 Given that  max Fx1, x2 = x1x22subject to    6x12 + 3x22 = 72 Part (c):- First order…