F(r, y) = is a homogeneous function of degree 1. True False

Q: If f(x,y,z)=xe^{4y}\sin(6z), then the gradient is

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Q: If x, y, and z are lengths of the edges of a rectangularbox, then the common length of the box’s…

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Q: The function f (x,y) = e* +3 tan – is a homogeneous function of degree_

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Q: If f(z, v) – 4z°y+ 8zy, then the total differential of f at z-1 and y - 1is: O df - 17 dz + 22 dy O…

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Q: Which of the following functions is homogeneous of degree 2/3. option I: 3 f(x, y) = /x² + y2 option…

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Q: Find the maximum and minimum values attained by f (x,y, z) = xyz on the unit ball ² + y² + z² < 1.

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Q: 1. Consider the function f(x, y, z) = x² + 2y + 2², which is differentiable at (2,1,1). 1) find…

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

Q: Find fr and fy- S(x, y) = /"9e" dt f.(r, y) : %3D f,(x, y) =

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Q: integrate ƒ over the given curve. ƒ(x, y) = x3&gt;y, C: y = x2/2, 0 &lt;=x&lt;= 2.

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Q: what can you lay about a continous Junction F:IR →0,0 f [M] s f (t) dt ?

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Q: Find the total differential of W = x^4 y^3 z^2 + x^3 Y^2 + x^2 z +y + 3 at (2,1,1)

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Q: Find the linear approximation to f(x, y, z) = at the point (–2, 3, 2) f(x, Y, z) ×

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Q: The function f (x, y) = e÷ + 3 tan is a homogeneous function of what degree.

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Q: Let y = 3x + 3x + 2. If Aa = 0.4 at x = 1, use linear approximation to estimate Ay | Ay a

A: We have to find the change in y using linear approximation

Q: (1) Use the Chain Rule to find dz/dt. (a) z = r² + y² + xy, r= sint, y = e'. z = x2 +y?, x = cost+…

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: Suppose f(x, y) =                             ((xy2) / (x2 + y4)), for (x, y) ≠ (0, 0)…

A: The given function is,

Q: Evaluate f, xyz dV, where Q = {(x, y, z): 0 < x < 2y, 0 <y< 1, 0 < z < x+y}.

A: According to question,Q = x,y,z : 0 &lt; x &lt; 2y, 0 &lt; y &lt; 1, 0 &lt; z  &lt; x+y

Q: f(x, y) = x*+ y* + 2 is a homogeneous function O TRUE O FALSE

A: We know that a function f(x,y) is homogeneous if  f(tx,ty)=t^nf(x,y)  is true for some integer n.

Q: Find the linear approximation to f(x, y, z) = at the point (2, –1, –2): f(r, y, z) z

A: A Givenfx,y,z=xyz at the point 2,-1,-2linear approximation at the point…

Q: Find the gradient of f(x, y, z) =e^y cos(xz) at (1,0,1) .

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Q: What is the integrating factor of the linear DE of order one ydx + (3x - 2y +5) dy=0,

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Q: Find the linear approximation to f(x, y, z) = " at the point (2, -1,1): f(x, y, z) z

A: Given the function

Q: If f(x) I (t° + 2t + 6) dt 0. then %3D = (x), ,f

A: The function needs to be integrated first and then to the subsequent function we will be double…

Q: The function f (x,y) =e/*+3tan( y/x) is homogeneous of degree A) 3 B) 2 C) 1 D

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Q: ]If x' +y +z =9, dx/dt 5, and dy/dt 4, find dz/dt when (x, y,z)=(2,2,1).

A: Topic- application of derivatives

Q: Suppose that x = x(t) and y = y(t) are both functions of t. If x2 + y2 = 25, and dx = 2 when x = 3…

A: Given that x=x(t) and y=y(t) are both functions of t . If  x2+y2=25           ..(1) Differentiate…

Q: Find the maximum and minimum values attained by f(x,y,z) = xyz on the unit ball x2+y2+z2 ≤ 1

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Q: Let f(x, y, z) = x² + 2y+ e³=2« + 2°. Find the rate at which f is changing at (1,2, –1) in the…

A: Use the formula of the directional derivative and simplify.

Q: Suppose x(t) and y(t) satisfy da = y? – 1 , dt dy = 2 – 2x. dt - - d (3x2 – 6x 0. + y³ – 3y) = Show…

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Q: Find fr and fy. 2e" dt f (x, y) = 2, f.(r, y) = f„,(x, y) =

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Q: The maximum rate of change of the function f (x, y, z) = x In(yz) at (1; 2; - is equal to: %3D O…

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Q: Find fz and fy- f(x, y) = Te“ dt f„(x, y) %3D S,(x, y) =| %3D

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Q: If f(r, y) = 3x2 – 8y, then the total differential of f at z = 1 and y=-2 is: %3D O df = 6 dx + 32…

A: we can find the total differential as below using the properties of partial derivative

Q: Find fr and fy. f (x, y) = 4e" dt f(x, y) = f,(x, y) =

A: A detailed solution is given below.

Q: a)Let z = x?y – y² where x = t2 and y = 2t . Find dz/dt at t=1 using chain rule.

A: Given query is to find derivative is nge chain rule.

Q: (c) Determine the degree of the following homogeneous function (0/(x,y) = 4x² + 2y, (i) f(x, y) =…

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Q: he The product of linear integration is where c t $ (2xy – x²) dx + (x + y²)dy, x = y? 30 y = x? ,…

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Q: x² +y² F(x,y) = is a homogeneous function of degree x- y

A: We have to find the degree of the homogeneous function

Q: Use the linear approximation of f(æ, y) = e+y at (0, 0) to estimate f(-0.03, -0.03)

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Q: Find the linear approximation to f(x, y, z) = " at the point (2, –1, 1): f(x, y, z) =

A: As per Bartleby guidelines for more than one question asked only one is to be answered please upload…

Q: Find div (e" grad u x 7) u=x-y ex at (2,1,0) where and =(x²+1)i + sec¯¹(x² −y)j + 3y²zk

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Q: Show that the function f(x, y) = x²y% + y° is homogeneous.

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Q: What is the integrating factor of (ry + y) dr + (r + 2y-1) dy %3D

A: Given xy+y2dx+(x+2y-1)dy=0Compare above differential equation with…

Q: Find fr and fy- f(x, y) = fetlo dt f.(r, y) = fy(x, y)

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Q: The function f (x,y) =e" + 3tan an( y/x) is homogeneous of degree А) 3 в) 2 cC) 1 D) 0

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Q: Let x",y" be the integrating factor of, (x'y² +3y)dx+(3x*y-x)dy = 0 Then, m (а) т%3—7,п-3D1 (b)…

A: We use this concept for solving given problem.i.e. integrating factor is a function used to solve…

Q: Verify the Pierre-Simon Laplace equation ∂2f/∂x2+∂2f/∂y2=0 with f(x,y)=ln∣x2+y2∣

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Q: Find f (1, 1) S(x, y) = In( %3D Vx² + y²

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