Determine the homogeneity of this function: f (x, y) = a+ a²y+7 3 O Homogeneous of degree 1 O Homogeneous of degree 3 O Homogeneous of degree 0 O Not homogeneous

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: Find linearization of the function f(x) = Vx + 3 at a = 1 and use it to approximate V3.98

A:

Q: Consider the function F(x, y) = x + 3x2 - 6xy? +2y3, Find critical points (FoC). Identify these…

A: Given function  F(x,y)=x3+3x2-6xy2+2y3 a. Differentiating F partially w.r.t to x and y, we get…

Q: Let f be a differentiable function satisfying the condition: f(x) for all x, y (#0) eR and f(y) 0.…

A: In this we have given a functional relations and from that we have to find out the function f(x), so…

Q: x² - y² z = g(x, y) = x² + y² 0 for for (x, y) = (0,0) (x, y) = (0,0)

A: Given function is z=gx,y=x5−y5x4+y4 for x,y≠0,00            for x,y=0,0. We have to check whether…

Q: Determine the value of m such that the function *- y - 2 E + 2 vỹ VI – Vy ; z +y f(x, y) = is…

A:

Q: Determine the set of points at which the function is continuous. a) f(x,y) = ln (x² + y² – 4)

A: According to question given thatf(x,y)=ln (x2+y2-4)

Q: Find the linearization L(x) to the function f(x)= Vx+4 at x =4, then use the linearization to…

A: linearlization of f(x) at x=a is  L(x) = f(a) + (x-a)f'a)

Q: Let f(z) = 3 Find (f-)'(x) using the formula %3D I+9 1 ((e) = and check your answer by…

A: I am going to solve the given problem by using some simple calculus to get the required result.

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

A:

Q: Find a non-zero function h for which F(x, y) = h(x)(x sin y + y cos y)i + h(x)(x cosy – y sin y)j is…

A: Given vector field is, Fx,y→=hxxsiny+ycosyi+hxxcosy-ysinyj.

Q: Find the linearization of the function f (x) = x' at x = 1. a ab Va |a| sin (a) 7 х-6 L (x) Using…

A: Given a function,

Q: Let f(x,y)=3x2-2xy+y2-8y  Find the absolute extrema over [0,1]x[0,2]

A: Consider the given function fx,y=3x2-2xy+y2-8y First, find the partial derivatives of the function…

Q: Show that the functions f (x) = I x I and g(x) = x 1/3 are not differentiable at x = 0

A: Derivative of x at x=0:   Plotting: x,  xx

Q: Find the linearization L(x) of f(x) at x = a. f(x) = Vx +15, a =7 %3D L(x) =

A: Givne that fx=x2+15, a=7To find L(x)

Q: Let f(x,y)=3x2-2xy+y2-8y  Find the absolute extrema over [0,1]x[0,2].

A: We have f(x, y)=3x2-2xy+y2-8y find critical points ∂f∂x=6x-2y=0 ... (1)∂f∂y=-2x+2y-8=0  ...(2)solve…

Q: Find the domain of the following multivariable functions b. f(x,y,z) = x/y+ In (z – 1) c. f(x,y,z) =…

A: Solution:Domain: The domain of a function is the set into whcih all of the input of the function is…

Q: Find the linearization of the function f (x) = xº at x = 1. L (x) = Using this linearlization, f…

A:

Q: Consider the function 23 – 3y if (x, y) # (0,0), f (x, y) = x² + y? if (x, y) = (0,0). Show that…

A:

Q: Consider the function g : Z x Z → Z × Z given by g(x, y) = (x+ 3y, 2x – y). Is g injective? Pr -…

A:

Q: Find the linearization of the function f (x) = x° 26 at æ = 1. a vā |a| sin (a) L (x) = Using this…

A: I am going to solve the given problem by using some calculus to get the required result.

Q: 1. Why is f not a function from R to R if a) f(x) = 1/x? b) f(x) = VT? c) f(x) = ±/(x² + 1)?

A:

Q: attached

A: Linearization of f(x) at x=a is given by

Q: 1. Find and sketch the doma in of the function. Ans A f(x,y) =Vy +V64 – x2 – y2 a. ((x,v)| 64 > x? +…

A: Given function is  f(x,y)=y+64-x2-y2 we have to find and sketch the domain.

Q: Determine whether the function 2х + 1 f(x) %3D 2r2 2x2 – x – 1 is continuous: a. at 2; b. at 1.

A:

Q: Find whether the function F-(* - y')i + (v² – 3x)j + (=* - xy)k is irrotational.

A: A vector field F is called irrotational if curl (F) = 0.

Q: Determine whether the function f (z)= Įz² – e3z I0

A:

Q: Let f ( x, y ) = ln ( ex * Y ) be a function. At which point the function is discontinuous? O a. (…

A: Given: f( x, y) = ln ( ex+y )     To determine: The point at which function is discontinuous.

Q: 11.2.4. f(x, y) = V]xy|.

A:

Q: Determine if the given function is continuous at x=a and if the function is differentiable at x=a…

A: Note: Since you have asked multiple question, we will solve the first question for you. If you want…

Q: Find the linearization of the function f () = z7 at z = 1. L (z) = 固助 Using this linearlization, f…

A: Given function is

Q: Show that the function F: C[0, 1] → R defined by F(f) = max f(x) zE[0,1] is continuous.

A:

Q: Find the Wronskian for the set of functions.{ex, e−x}

A: Given set of functions ,f1=ex & f2=e-x

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

A:

Q: Consider the function: f(x)= (5/x^3)-(4/x^7), x>0   Let F(x) be the antiderivative of f(x) with…

A: Consider the function It can be written as

Q: f(x,y) = x2 + 2xy - y? is an example of homogeneous function. OTRUE O FALSE TRUE FALSE

A:

Q: Use FunCtion 9(x) = - f (X)tZ gra ph Of Y = fLX) to g raph Y=F(x) 2十 -4

A:

Q: Determine the homogeneity of this function: f(x,y) = x4 - xy3 +1 O 1 4 This is not a homogeneous…

A:

Q: Find the domain of the function. f(x, y) = Vy- 2x In(y + 2x) %3D Ox 2 O -y 0 O -y 2x O x > 0, y >…

A: We need to find the Domain of   f(x,y)= √(y-2x)ln(y+2x) The solution is given below.

Q: Let f be an invertible differentiable function satisfying 1 f(a) =b, f'(@)=+² 1+a²° 1 Then (f-1)'(a)…

A: Given: f be an invertible differentiable function satisfyingf(a)=b, f'(a)=11+a2 To Find: f-1'a…

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 linearization L(x) of the function at a. п f(x) = sin(x), a = 6 L(x) =

A:

Q: For the function f(x, y) = xy((x2 − y2) /( x2 + y2) ) define f(0, 0) such that f is continuous at…

A: A function f is continuous at the origin, the function value at the origin must be equal to the…

Q: Determine the value of m such that the function x- y - 5 E + 5 VI - Vỹ f(x, y) = is continuous at…

A:

Q: Find the linearization L(x) of the function at a. f(x) = sin(x), a = %3D L(x) = %3D

A:

Q: Consider the function z = f(x,y). If fx(a,b) and fy (a, b) both exist, and they are equal, then the…

A:

Q: Find the values of a and b such that f is differentiable at x = 3

A: Given,            The function is fx=ax+bx≤32x1-1x>3To find : Find the values of a and b such…

Q: Find the domain of the function f(x, y) = ln(8 – x° ? – 4y²). | - > 1} 2. {(r, v) : + 1} 4. {(x, v)…

A: We need to find the domain of the given function.

Q: 10.3.13. f(x, y) = xy ln(x² + y²).

A:

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

A: Given average revenue defined as function R¯x=Rxx   x>0 To prove if a revenue function Rx is…

Minimization

In mathematics, traditional optimization problems are typically expressed in terms of minimization. When we talk about minimizing or maximizing a function, we refer to the maximum and minimum possible values of that function. This can be expressed in terms of global or local range. The definition of minimization in the thesaurus is the process of reducing something to a small amount, value, or position. Minimization (noun) is an instance of belittling or disparagement.

Maxima and Minima

The extreme points of a function are the maximum and the minimum points of the function. A maximum is attained when the function takes the maximum value and a minimum is attained when the function takes the minimum value.

Derivatives

A derivative means a change. Geometrically it can be represented as a line with some steepness. Imagine climbing a mountain which is very steep and 500 meters high. Is it easier to climb? Definitely not! Suppose walking on the road for 500 meters. Which one would be easier? Walking on the road would be much easier than climbing a mountain.  

Concavity

In calculus, concavity is a descriptor of mathematics that tells about the shape of the graph. It is the parameter that helps to estimate the maximum and minimum value of any of the functions and the concave nature using the graphical method. We use the first derivative test and second derivative test to understand the concave behavior of the function.