Part I Determine in each question whether or not the function is homogeneous. If it is homogeneous, state the degree of the function. d. x-y e. (x* + y* )e +4xy f. xsin y sin

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: Which of the following function/s is/are homogeneous? a) x3+x2y+x3 b) lnx-lny-ex/y c) ex d) 1/…

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Q: Question 7. Šolve I. D²u – u = f(x), u(-x) = u(x) = 0, -0∞<r < x, by finding the two-point Green's…

A: Given that,  Dx2u-u=f(x)u-∞=u∞=0 Now , The auxiliary equation is m2-1=0m=±1 u=C1ex+C2e-x Take ,…

Q: A function of the form y ax + bx + c, a + 0, is called a/an function.

A: The given function is, y=ax2+bx+c, a≠0 For the given function, the degree of the function is 2.

Q: 2. Find and classify all the extrema of the function f(s, t) = (4s² + 2t²)e¯

A: 2

Q: Q1: Find and sketch the domain for each function. 1 2. f(x, y) = In(4-x²-y²) 2. f(x,y) = cos ¹(x −…

A: Given: The functions are:               1. fx,y=1ln4-x2-y2               2. fx,y=cos-1y-x2  To find:…

Q: Find the Linearization L(x) of the function f(x) = 3√1 +x a = 0 and use it to approximate the…

A: Let's find.

Q: of of H.W: Find and for the functions: Ox ду 1. f(x, y) = (xy – 1)? 2. f(x, y) = x² - xy + y? | 3.…

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Q: Exercises 1. Integrate each of the following functions with respect to r: (a) rº, (b) r'/2, (c) r3,…

A: Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: 2x The function f (x,y) = is said to be homogenous to what degree? A non-homogenous function B) two…

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Q: The function f(x) = x^3 + 2xy^2 - (y^4)/x is homogeneous of what degree?

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Q: Find and sketeh the domain of the function f(x, y)= ln| xy - 1 Vy-x² ху —1

A: Given: fx,y=lnxy-1y-x2 to find the domain and sketch the domain of the function.  The domain is the…

Q: Which function is continuous? 1 A(x)% = C(x): H %3D %3D x² + 2x + 1 1 1 G B(x) = J D(x) = x² - 2 %3D…

A: To find which is a cotinuous function?

Q: x* - 2y* (d) Is the function f(x)=- Vx +. homogeneous? If, yes, then find the degree of f(x).

A: We have to examine that the given functions  is homogeneous or not

Q: Question No. 03 Let f(y) = Vy and g(y) = y +1 Find..... i). f(g() =? i). f(g(4) =?

A: Find f(g(y)) and F(g(4))

Q: (2² + ,2) u+v (1² – 4v 2 2,.(x) 3/2 12

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Q: Which of the following is a non-homogeneous function? A f (x,y) = x3 - x y + y³ f (x, y ) =(y² + x²)…

A: A function f(x, y) in x and y is called homogenous function if degree of each term is equal.

Q: I. Determine if the function is homogeneous. 1. еx 4. x2+2y2 2. tan x x2+3xy 3. 5. (u² + v?) x-2y 6.…

A: Using definition of Homogeneous of a function check each parts.

Q: Which of the following function/s is/are homogeneous? d) 1/ (2√x+y) e) ln(x-y) f) x/ (√x2-y)

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Q: Differentiate the function. g(t) = In(5 + t“) g'(t): %3D

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Q: What is the degree of the following homogeneous function? f (x, y) x + 3xn-kyk + yn X2 x² - y²

A: The degree of homogenous function fx,y is n such that for constant t we have: ftx, ty=tnfx,y We…

Q: Find the number of zeros of f(z) = z3 + z* + 2z2 + 1 in the first quadrant. %3D

A: Given that,     fz=z13+z4+2z2+1

Q: 3: Assume that g(s) is an increasing function and define f(x, y) = g(x² + y²). Show that the angle…

A: Use definition of angle between vectors and gradient of function

Q: (a) Find the local extreme values of the function f(x, y) = 2xy – x² – 2y² + 3x + 4.

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Q: Use Theorem 7.1.1 to find (ft)). (Write your answer as a function of s.) f(t) = (et-e-t)² L{F(t))

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Q: Let a + 0 be a constant. Give an example of a function y = f(x) for which ay – y' = 0 and g?y – y" =…

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Q: Find a, b, and c for the function f(x) = a sin(bx – c) such that the graph of f matches the figure.…

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Q: Question 1 A. The multivariable function f (x, y) = 3x² + 2xy – 7y² + 13x 6y + 4, find: i. f(x, y)…

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Q: .2 x + y F(x, y) = is a homogeneous function of degree

A: We have to find

Q: 8) Find the x-coordinates for the points of inflexion of f(x) = %3D a) O x = 0, x = 1 b) O x = 1…

A: fx=x412-x36     f'x=4x412-3x36             =13x3-12x2      f''x=4×3x212-3×2x6=x2-x=xx-1    So,…

Q: Find the absolute maximum for the function f(x) = re, xE [-1,3] %3D 3e Зе e 2 4

A: We need to find the absolute maximum of the function f(x)= (x2e-x)/2 on [-1,3]. The solution is…

Q: J 3(x)is even function 0 صواب ihi O

A: We will use the fact that j_-n(x) =(-1)^n j_n(x) to decide whether j_3(x) is even or odd function.

Q: 1. For what value of x does the function g(x) --x + 2x strictly concave downward? %3D 3. B. x > 1 A.…

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Q: A/ Derive by definition: y = Vx - 3 ? B/ Determine the value of (z) and (k) that makes the function…

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Q: Find f(x) and g(x) such that h(x) = (f • g)(x) a. h(x) = V5x – 2 b. h(x) = 19x² – 4| c. h(x) = tan…

A: Authoring guidelines: As per the authoring guidelines we can solve only the first three parts of…

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

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Q: Question 12 Find the linear approximation of the function f (x, y) = 2x – y + a²y - near the point…

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Q: Find the functions (a) f ° g  , (b)  g ° f , (c)  f ° f  , and(d) g °g  and their domains.   f(x)  =…

A: Consider the given function as fx=1-3x, gx=cosx

Q: Suppose that h(x) = f(g(x)) and g(3) = 6, g'(3) = 4 , f(3) = 2, f(6) = 7. Find the value of h'(3).…

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Q: x2 ,0<x<2 let f (x) , find a %3D -x+6 , 2<x<6 24 9 8. .b O 9. 16 9. 32 .d O 9.

A: given function is                                   f(x)=x2       ; 0≤x≤2-x+6 ; 2≤x≤6 we have to…

Q: The function y=C, e° is the general solution of a) O y"– 2 y' – 3 y = 0 b) O y" +2 y' – 3 y= 0 O y"…

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Q: 1. Find the values of a, b, c, d such that the function f(z) = x² + axy + by² + i(cr² + dxy + y²)is…

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Q: 2x² + y² x + 2y In (x + y)+ y tan In 3x - y

A: Given function is  fx, y=xln2x2+y2x-lnx+y+y2tanx+2y3x-y We have to determine whether the above…

Q: The function h(x) (z + 4)° can be expressed in the form f(g(x)) where f(x) = r°, and g(x) is defined…

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Q: Find the linearization L(x) of the function at a. 3 f(x) = Vx, a = 64 %3D L(x) =

A: We can find the linearization as below.

Q: Find the linearization L(z) of the function f(x) = 1+ 2x+5 at z =1. Answer: L(z)

A: topic - linearization of a function

Q: Determine whether or not the function is homogeneous. If it is homogeneous, state the degree…

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Q: Find a function g = g(t) such that %3D s +3 L(g) = s2 – 2s + 5 -

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Q: Question a) b) Let f(x, y) = 2√x - y²e-²xy + ²/3. Find fx and fy. Evaluate fxxy(4, -1).

A: Given: For (a),     ∂ ∂ x2x-y2e-2xy+2y=∂ ∂ x2x-∂ ∂ xy2e-2xy+∂ ∂ x2y=1x--2y3e-2yx+0=2e-2xyy3+1x    ∂…