company has S300,000 spend on two products. Suppose by the company from x units of the first product and y units of the second product is given by Show that U is homogenous to some degree . Show that Euler's Theorem holds for the function U(x,y).

Q: a4A Function is said to be homogeneous if it fulfills the condition f Ctx,ty) (大)すt O true O Error

A: We will justify that given statement is true or false.

Q: Show that the functions have exactly one zero inthe given interval. g(t) = 2t + √1 + t - 4, (0, ∞)

A: g(t) = 2t + √1 + t - 4,              x ∈ (0, ∞)    g(t) = 2t + √(1 + t)  -  4

Q: Verify Eular's Theorem for the function xy+yz+zx

A:

Q: Find the maxamin s in flectlon Points and the in ter Vals on which the function inerease,decrease…

A: follow the solution which is mentioned in step 2.

Q: Suppose that y and z are twice-differentiable functions of r. Show the d y dr y z %3D y"

A:

Q: Consider the function f defined by 1²+y² V12+y?+1-1 ,2 f(r, y) = %3D lim(7.y)¬(0,0) f(x, y) =

A:

Q: Find two positive numbers x and y such that x+y=60 and xy^3 is maximum.

A:

Q: Find the domain of the function f(x,y)=arccos(x²+y²-49360). O {{x,v) E R² | x,y € R}. O {(x,y) € R²…

A: Consider the function fx,y=arccosx2+y2-49360. Here, the objective is to find the domain of the…

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A:

Q: 9. Use the chain rule for multivariable functions to find where f(u, v) = u + v u(x, v, z) = x+y,…

A:

Q: Find the antiderivative Fof f that satisfies the given condition. Check your answer by comparing the…

A:

Q: : Express the function f (x) = e") to the form u(x,y) + iv(x,y).

A:

Q: Consider function f(x,y) for which = 24x2 + 114y and = 114x + 24y². Which of the se ду %3D əx points…

A:

Q: 11. Verify that the conclusion of Clairaut's Theorem holds for the function: f(x, y) = e*Y sin(y)

A: The given function is: fx,y=exy siny To verify that the conclusion of Clairaut's theorem hold for…

Q: Find the MRSxy of the utility function U=In(x)+y.

A:

Q: here r jl and nl is a function of x or k i m very confused can u please explanion

A: The function is,................ j2x=π2xyi+12xη2x=π2xNi+12x

Q: 4. Integrate the function f(z) = z² + 2z from z = -i to z = 1 in two ways, once along a straight…

A: The objective is to integrate the function fz=z¯2+2z from z=-i to z=1 in two ways, Once along the…

Q: Find linearization L(x) of f(x) = tanh=' at a= 0 and use it to estimate f(0.01).

A: Topic:- linearisation

Q: 2. k) Show that fe2) = function is analytic %3D t'+s for Rez 70.

A: Calculate the limit: lim∆z→0fz+∆z-fz∆z=lim∆z→0∫0∞e-tz+∆zt2+1dt-∫0∞e-tzt2+1dt∆z…

Q: Picture attached. Thanks in advance!

A:

Q: Consider the function f(x) = 3z10 + 3z° – 3z² – 4. Enter the general antiderivative of f(z)

A: Given function is : f(x)=3x10+3x5-3x2-4 We have to find antiderivative(integral) of the given…

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Q: Find given that z is a differentiable function of x and y, and xz + yz3 = 2 +x²ev

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Q: . Suppose that F(t) is a twice-differentiable function of one variable. Define the function f(x, y)…

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Q: Let f(x, y) be a positive function. Let 1 1 1 I2 = ||f(x, y)dydx 23 1 1 I3 f(x, y)dydx Then I < I2 <…

A: We first find the area represented by the given limits of integrals. This area will hold for any…

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A:

Q: Suppose that F(t) is a differentiable function of one variable. Define the function z(x, y) = e"F…

A: Given that zx,y=eyFexy where F(t) is differentiable function . Prove that xzx+yzy=yz

Q: Find for the function h(x, y, z) h(x, y, z)= ecos(y +8z).

A: Given,           hx,y,z=e7xcosy+8x

Q: x + y + 1 f(x, y) = , x ln (y² х — 1 -

A: A function f=f1, f2, ⋯, fn is said to be continuous at a if and only if the all the components f1,…

Q: Use Lagrange multiplier to find the indicated extrema, assuming that x and y are positive. 6.…

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Q: Q4: integrate the following function f(x,y) for x from z to 2n and for y from 0 to f (x, y)=…

A:

Q: Find the domain of the function f(x,y)=V13032-x + y-> {(x,y) E R2 | y# x2 and ys 13032}. O {(x,y) E…

A: Given, fx, y=13032-x+1y-x2

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A:

Q: Q, Frd the donain of H fallowing function: fa) = 5x -3x-4

A:

Q: Find the antiderivative F of f that satisfies the given conditions. SHOW WORK!!! 1. 4Vx + f(x) = ;…

A:

Q: Solve this attachment.

A: Given:fx,y=xy2-x2-y

Q: 3. Find the lincar approximation of the function g(x) = V1+x at a = 0 and use it to approximate the…

A: Use taylor form

Q: ew Choose the definition for the function. S-x+2 x > 1 lx+1 a. y = { {-x+ 2 x 1 b. y = {x+1 1-x +2…

A: Since function is not continuous at x=1 because graph of function is break at x=1 so, right and left…

Q: Find the linear approximation of the function at the give f(x.y) = 3x y at (- 6,9) O A. L(x,y) = -…

A:

Q: Suppose z = ƒ(x, y), where x and y are functions of t. How many dependent, intermediate, and…

A: It is observed that z=fx,y is function of x and y.

Q: b) Let f(x) be the linear function so that the straight line y=f(x) passes through the points (0,1)…

A:

Q: Suppose that f: R2R is a function given by S x²+y² f(x, y) 0 for xy = 0. Show that f(x, y) is…

A: We have to show the given function  f(x, y) is continuous  at ( 0,0)

Q: 1. Show that the function x2 – y2 2xy f(x,y) ={ x2 + y? if (x,y) # 0 if (x, y) = 0 is continuous at…

A: If for every ε&gt;0, there exists a δ&gt;0, such that if |x-a|&lt;δ, |y-a|&lt;δ, then the function…

Q: Find the local linear approximation L (x)of the function f (x) = lnx at x = 1 %3D

A: LINEAR APPROXIMATION

Q: The average revenue is defined as the function R(x) Ř(z) (x > 0) Prove that if a revenue function…

A: Let Rx denotes the revenue function. The average revenue function is defined by Rx=Rxx where x&gt;0.…

Q: xyz f(x.y.z) = et ot function is given P(2,,4) in point fux + fyy + fzz colculate.

A:

Q: of of For the function f(x,y) = In (x+ 3y), find and dx df of ду II

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.