of of Find and for the furction f(xy,z) = x y+ y + xỉ ôx 'ay

Q: biven that y=sin(3lncx)) is a solulion of x y" + xy' +9y=0, solue x y"+ xy' +qy=0 ; y()= 2 =y'().

A: Solve Cauchy Euler differential equation

Q: xy Prove that the function f(x, y) is differentiable everywhere in its do- x² + y? main.

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

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Q: Calculate the second order differential of the function f(x,y) = x^{4}*y^{2}+2*x-y^{7}+3 Attached…

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Q: a) Find the directional derivative of a(r, y) = 3-y at (1, 1) in the direction (-3,4). b) Find and…

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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: Value of divergence of function (x2y2)î - (z³y 4x) ĵ + 4y² xk at (1, 2, 1) is

A: Given vector is (x2y2)i^ - (z3y-4x)j^ + 4y2xk^

Q: f(x) = x² + sin z %3D is an antiderivaive of Athat satisfies F(x) = 0.| %3D

A: Given;- fx=x2+sin x   Solution:- ⇒∫x2+sin x dx ⇒∫x2 dx+∫sin x dx ⇒x33-cos x ⇒x33-cos x+C…

Q: Illustrate local linearity for the function f (x) = xsinx at x = l.

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Q: Is the function f(x, y) = ||x| - |y|| - |x| - |y| differentiable at (0,0)?

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Q: Jerify Divergence Theorem for F = = (x + y') i – 2 xỷ + 2 yzk and the volu

A: Given: F⇀=(x+y2)i^-2xj^+2yzk^The plane, 2x+y+2z=6

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

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Q: UNIVERSIT b) Given z = f (x – y, 2x – 2y, 3x – 3y). Show that - dz dz + = 0. dy

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Q: Find f-(x, y) and fy(x, y). f(z, y) = (y° tan(5z)) f-(x, y) fy(x, y) =

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Q: Let x and y be differentiable functions of t and lets = sqrt(x2 + y2) be the distance between the…

A: Given that, s=x2+y2

Q: (b) A bounded, 3B > 0 such that |f(x)| < B Vx € (0,1), continuous function on (0,1) with unbounded…

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Q: Assuming that z is a differentiable function of x and y, Let F(x,y,z) = ln(x²y) - e* -tan-¹ z. Find…

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Q: 2. If F(x, y, z) = 2z3 – 3(x² + y²)z, then verify that Frx + Fyy + F2 = 0. %3D

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Q: Solve ux – uy +yu = 0, where u is a function of x and y. %3D

A: Given: ux-uy+yu=0. The objective is to solve u, where u is a function of x and y.

Q: Find fzyz. f(r, y, z) = x*y³zª + xy" + y°z f zyz

A: Given-  fx,y,z=x4y3z4+xy7+y6z To Find- fzyx

Q: uppose that F(x, y, z) = 0 defines z as a function of x and y and F is differentiable. "rove that dy…

A: Given F(x,y,z)=0

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…

Q: Find fzya. f (r, y, 2) = x°y*z" 5.8 + xy* + y°z %3D f zyz

A: Given data÷

Q: Find fzyz. f (x, y, z) = x°y°z° + xy7 + y®z f zyz ||

A: Using derivative,

Q: Groph of f(x)= (x² Is there a Is f differentiable at X=o? Justify %3D sharp Corner at X=O ?

A: Consider the given graph. fx=x2+0.0001 Now, draw the graph.

Q: (3) Consider the derivative dz = 2xydx + (x² + 2y)dy Evaluate whether this is a total derivative, by…

A: We will check whether the given function is total derivative or not. We also integrate dz pathwise.

Q: The directional derivative of the fiunction f (x, y, z) = x²z+ xyz + y² in the direction of u = 2i +…

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Q: stlon 5 Use differential to approximate the change in the value of f(x)= ° as e goes from 2 to %3D…

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Q: Find fr and fy- f(x, y) = 7e dt f-(x, y) = f,(x, y) =

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Q: continuous function h(x),

A: Differential equation

Q: f(x, y, z) = e-3zyz 三 fy = 三 ニ f.

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Q: 3) Caputo derivative of order yof a [y] differentiable u function with y> 0 is given t 1 çDYu(t) =…

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Q: uestion 4 Assume that all variables are the function of t. If 5x2 - 4y3+3y=7 and dy/dt =6 when x-13…

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Q: Dete‎rmine if f (x, y) = ={(xsi‎n3y)/(x‎2+y6), (x, ‎y) ≠ (0, ‎0) ={1, (x, y) = (0, 0) is‎…

A: Solution: A graph for a function that's smooth without any holes, jumps, or asymptotes is called…

Q: Find all the first and second order derivatives of the function f(x, y) = x³ ln(y) + xy + x³y² + 4x…

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Q: prove that xy^2/x^2+y^2 is not differentiable at 0,0 when  xy^2/x^2+y^2 if (x,y) not equal to (0,0)…

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Q: Find fz and fy- Te dt f(x, y) = 5 f.(x, y) f,(x, y) : %3D

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Q: 2. Find the directional derivative of f(x, y) = -2e* cos y at %3D (0, ) in the direction of v = (-6,…

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Q: Classify the point (1, 1) for f(z, y) = zye" 2 by using Second derivative test if POSSIBLE. Lütfen…

A: Given that,                  fx,y = xye-x2-y22 . We have to classify the point 1 , 1 for fx,y by…

Q: Find the rate of change of f (x, y, z) = 3xyz in the direction normal to the surface yx² + xy² + yz²…

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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: 2. Let closed curve C consist of the line segment from (0, 0) to (2, 1), followed by the line…

A: We will solve both parts of this question using basic knowledge of line integrals and definite…

Q: Find div F if F(x, y, z) = (x² + y)i + z²j + (eY - z) k.

A: Our Aim is to find the value of div F if F(x,y,z)=x2+y i +z2 j+ey-zk -(i)Let  F(x,y,z)=x2+y i +z2…

Q: 3- Verify the properties (HINT Use integration by parts) F[ux] = iF[u] F[uxx] = -²F[u]

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Q: integral that line x = 0

A: As per the bartleby guidelines for more than three parts only three has to be solved. Please upload…

Q: tor. f(x,y)= In (8+3x²+3y²); P(3,-1); (3.2) d the gradient of f(x,y) = In (8+3x²+3y²). xx,y)=

A: Topic:- application of derivatives

Q: /alue of divergence of function (x2y2)î - (z³y – 4x) ĵ + 4y2 xk at (1, 2, 1) is

A: Let f = (x2y2)i^ - (z3y-4x)j^ + 4y2xk^

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

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Q: Let x and y be differentiable functions of t, and lets = √(x2 + y2) be the distance between the…

A: Given equation is s=x2+y2. Compute the derivative of s with respect to t.…