Determine if the following are homogeneouS or non-homogeneous functions f (x, y) = x In x – x In y f (x,y) = e*

Q: 1- f(x,y) = In(x² + y?) at (1,1)

A: As per our guidelines we are supposed to answer only one question. Kindly repost others question as…

Q: About what point is the local linear approximation l(x): of the function f(x) = tan x valid? 4

A: According to question, Local linear approximation,lx = x2 +π4-12,         .......1Given Function,fx…

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

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Q: 12. Consider x²y f(x, y) = g4 + y? for (x, y) (0,0) and zero otherwise. Is f continuous at (x, y) =…

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Q: f(x) is a positive continuous function on R what does the function F(x)= | f(t) dt a represent (for…

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Q: iven F(x) = L- (1 – /1– (1+1)² ) dt valuate F(0) and F'(/2) using the First Fundamental Theorem of…

A: We have to find out

Q: Let f(x, y) = ln(x + y − 1). Then, ƒ(e, 1) =

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Q: Suppose that z is a differentiable function of x and y with dz (2, 5) = 108 and- dx dz (2, 5) = 9.…

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Q: f(z) is a twice differentiable function with f(0) = 1, f(2) = 4, f'(2) = 5, Then af"(x)dx = %3D

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

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Q: Assuming that z is a differentiable function of x and y, Let F(x.y.2) = In(x³y) – e" -tan-z. Find F,…

A: We can find the answer as below.

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

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Q: Determine if the following are homogeneous or non-homogeneous functions f (x, y) = cos = cOS x + y f…

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Q: 23. Find the most general antiderivative of the functions: a) f(x) = 1 –- x³ + 5x5 – 3x7. 5 – 4.x3 +…

A: Given: 1.fx=1-x3+5x5-3x7 2.g(x)=5-4x3+3x6x6 we want to calculate the antiderivative is nothing but…

Q: Differentiate f(x) with respect to g(x) of yx=xsiny

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Q: Find the linearization of the function f (x) = x at x = 1. a lal sin (a) L (x) Using this…

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Q: Let f(x) x2 + 1 Enter an antiderivative of f(x)

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Q: 2. Find the gradient of the function f(r.y) In(r y²) at the point( 1, 1).

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Q: Find and classify all critical points for the function f(x, y) = x + y – 4xy + 2 %3D

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Q: 4. Suppose that F(t) is a differentiable function of one variable. Define the function z(x, y) = e'F…

A: z(x,y) ey F (exy )diff wrt xdzdx = ey F' ex/ye.1/yzx = ey.ex/yyF' (ex/y)and diff wrt ydzdy= ey…

Q: Find the center of mass of the thin plate bounded by the graphs of the given functions. g(x) =…

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Q: Find a function f (x, y, z) such that ∇f =〈z, 2y,x〉.

A: Given that, ∇f=z,2y,x We have to find a function f(x, y, z) such that ∇f=z,2y,x. Let us consider,…

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

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Q: Find linearizing ( L(x) ) f(x) at x=a . where f(x) = tanx and a = π a) π b)  x - π c) π - x d)…

A: SOLUTION-

Q: If f(x,y,z) = z In(x²ycosz): then fz is

A: Here, the given function is: f(x,y,z)=z ln(x2ycos z) Using the properties of the natural logarithm:…

Q: Consider the For at function y= In(x+1) . what valves" of x is y undefined ?

A: The given function is y=ln (x+1). The objective is to determine for what values of x is y undefined.…

Q: Find the best linear approximation to f on th e interval [0, 1].                            f (x)…

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Q: 3.Find the linear approximation to f(x) = cos x at x, = ÷ and use the linear approximation to…

A: We will use formula for linear approximation.

Q: Test the given function for its homogeneity. If it is homogenous, give its degree. f (x, y) = x + y+…

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Q: Find the particular antiderivative F(x) of f(x) = x + that satisfies F(1) = 3. %3D

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

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Q: Let f (x, y, z) = ln(x2 + z) + y2 exz. Find fzyx

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Q: I. Show that the function ƒ defined by (1, y) = (1, –1) f(1, v) = { +g (z, y) # (1, –1) + y is not…

A: We will use the sequential characterization of continuity to solve this problem. The detailed…

Q: 1. Integrate the function f(x, y) = x – y over the triangle T with vertices (0,0), (1,0), and (1,2).

A: Given triangular region is bound by the vertices 0,0, 1,0 and 1,2. The sides of the given triangular…

Q: Verify Young's Theorem S. f(x, y) = = e(2x+y) In(xy)

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Q: Find the best linear approximation to f(x) = ex on the interval [-1,1]

A: We have to find the best linear approximation of f(x)=ex on the interval -1,1.

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: 5.) Use linear approximation to estimate f(0.1, −0.9) x² sin x In(y² + 1) Y f(x, y) = of th + x+1…

A: NOTE: Refresh your page if you can't see any equations. . here we want to find the approximate…

Q: (d) The function x²+y? Vx2+y? (x, y) # (0,0) f(x, y) (x, y) = (0,0) is continuous at (0,0).

A: Note: according to Bartleby policy we are allowed to write only one question please post remaining…

Q: find ∇f at the given point. ƒ(x, y, z) = x2 + y2 - 2z2 + z ln x, (1, 1, 1)

A: Given function is fx,y,z=x2+y2-2z2+zlnx and point=1,1,1

Q: 6. Find the gradient of f(x,y) = ,x' - u°. grad f i +

A: We will find the first order partial derivatives with respect to x & y and use the definition of…

Q: Find the antiderivative F for f(x) = | sin z|, -T <x <0 satisfying F(0) = 1. (1) F(x) = - cos x – 1…

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Q: If z=f(x,y), x= r cos θ and y= sin θ, where f is a differentiable function expressing az/ax and…

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Q: (b) Determine whether (x, y) # (0,0) (r, y) = (0,0) f(x, y) = continuous or not.

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Q: Let L(r) be the linearization of f(x) = sin x + 1 at the point x = . Find L(π/2).

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

A: LINEAR APPROXIMATION

Q: 2. The function f in |f(x)dx = F(x)+C is called A. integral B. derivative C. antiderivative D.…

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Q: Find the linearization L(x) of f(x) at x = a. f(x) = sin x, a = 0 O L(x) = 3x + 1 O L(x) = 0 O L(x)…

A: L(x) = f(a) + f '(a) (x - a) where, L(x) is the linear approximation of f(x) at x = a. f '(a) is…

Q: if (x, y) # (0,0) (1 if (x,y) (0,0) x+y (a) Prove that the function f(x, y) =2x+y is not continuous…

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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&gt;0 To prove if a revenue function Rx is…