Do not simply the answer. Determine ∂2z/∂x2 given that z is a differentiable function of x and y, and xz + yz3 = 2 +x2ey.

Q: Please show step-by-step

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Q: Describe the level surface F(x, y, z) = 0.…

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Q: Find div F and curl F if F(x, y, z) = xz°i + 2y°r*j+ 6z*yk. div F=2° + 16 y' x+ 12 zy curl F=

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Q: The equation of tangent plane to the surface f(x,y, z) x+ y +z-9 0 at the point (1,2,4) is x+y+z=…

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Q: The tangent plane to the surface with equation at the point where (x, y) = (1,0) has the equation z…

A: According to guidelines I solve the first question only.So kindly request you to repost the…

Q: Sketch a typical level surface for the function. 10) f(x, y, z) = /x2 –z %3D

A: sketch a typical level surface for the following 10) fx,y,z=x2-z it is known that level surface is…

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Q: Let f(x,y)= ysin x+ tan¯'(xy). Determine: (a) fy(x,y). (b) fyx(x, y).

A: Given f(x,y) = y sinx + tan-1(xy) (a) We need to find fy(x,y)  Hence we will partially differentiate…

Q: Let u(x, y) = e" (x cos y – y sin y). Find all analytic functions f : C → C such that the real part…

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Q: c) Verify Stokes's Theorem for F = (x²+y²)i-2xyj takes around the rectangle bounded by the lines x…

A: Stoke's law is given as ∫cF→.dr→=∫s∫∇×F.n→ds F=x2+y2i^-2xyj^ dr→=(dxi^+dyj^) So F.dr=x2+y2dx-2xydy…

Q: Describe the level surfaces for f (x, y, z) = y+10-√√x² + z² and sketch them for several (at least…

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Q: Assume that f is a de ferentiable function with fax (5,0) =6 and fu(5, )=4. Let w Cu,v) =f (x (u,v),…

A: Given,w(u,v)=fxu,v,yu,vx=6 cos u+5 sin vy=7 cos u sin vfx(5,0)=6 and fy(5,0)=4 To find:wuπ2,π2

Q: 35. f(x, y) = x+2y2 -x; R is the disk x2+ y? < 4.

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Q: Describe the contour map of f (x, y) = x with contour interval 1.

A: Consider the function fx,y=x. we know that the level curves of a function fx,y are the curves in the…

Q: Evaluate F.dr where F(x, y) = xy i+ej and Cis the line segment from (2, 0) to (4, 0).

A: From Stoke's theorem:   ∫CF·dr=∫F1dx+F2dy+F3dz   Given: Fx,y=xyi+exjLine segment;2,0to4,0

Q: Display the values of the function in two ways: (a) by sketching the surface z = f(x,y) and (b) by…

A: Given the function is fx,y=9x2.

Q: Sketch the surface given by the function. z = 9-x?-y?

A: Given, z=9-x2-y2

Q: Given a surface f(x,y) = -2x² + (-3)y“. Find the derivative in the direction of v = at the point…

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Q: (B) Find analytic function f(z) =u+iv such that, d Im dz 2x +e* cos y is analytic function. R %3D .2…

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Q: Describe and draw at least 3 level surfaces for the function f(r, y, z) = x²+ y? - z?

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Q: Describe the level surfaces for f(x, y, z) = y+10-√x² + z² and sketch them for several (at least two…

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Q: find the gradient of function f [x, y,z] = 3x² -y?_z? at paint {i,-Ź, -¡}

A: The given function is fx,y,z=3x2-y3-z2 and the given point is 1,-2,-1. The gradient of the function…

Q: Evaluate / = F dr where F [y+z, z+x, x+y] and C: r(t)= [t, sint, cost], from A:(0, 0, 1) to B:(T, 0,…

A: Answer

Q: he figure shows a curve C and a contour map of a function f whose gradient is continuous. Find Vf•…

A: To Determine: find ∫C∇f.dr Given: The figure shows a curve C and a contour map of a function f whose…

Q: Consider two functions u(xyz) and v(xyz), where r, y, and z are independent variables. What is Vu x…

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Q: Find div F and curl F if F(x, y, z) = xz°i+ 4y°x²j+ 22²yk. %3D div F=|2 + 12 y² x² + 4 z y curl F=|2…

A: Find div F and curl F

Q: True or false (Provide/Show Justification for answers) (a) f (z) = |z|² is differentiable at zero?…

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Q: What kind of surfaces are the level surfaces f(x, y, z) = const? f = 4x - 3y + 2z

A: As per the question we are given a trivatiate function : f(x, y, z) = 4x - 3y + 2z And we have to…

Q: Find div F and curl F if F(x, y, 2) = 17y*z*i – 3a*2®j – 3ry®k. div F= curl F=

A: Divergence of F: ∇·F=i→∂∂x+j→∂∂y+k→∂∂z.i→17y4z4-j→3x3z6-k→3xy6 ∇·F=∂∂x17y4z4+∂∂y-3x3z6+∂∂z-3xy6…

Q: Consider that y is a function of x, then (x – h)? + y² = r² where r is a parameter. %3D -

A: We have to obtain the differential equation of the following equation, (x-h)2+y2=r2 Where r is a…

Q: find the directional derivetive of f (X, Y) = 3x² + 5y² at the point (1,-1) in Hhe Acrection of V…

A: To find the directional derivative of fx,y=3x2+5y2 at the point 1,-1 in the direction of v=-4, 3

Q: Fx to find dy Assuming - 7x - 9y2 - 2xy = 0 defines y as a differentiable function of x, use the…

A: To find the derivative using the theorem

Q: Use the function to show that f(0, 0) and f(0, 0) both exist, but that f is not differentiable at…

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Q: Consider the function f(r, y) = 21? + ry – 6zy + 5x +2. (a) Show that (1,3) is a stationary point of…

A: Find the maximum and minimum, using send derivative test.

Q: -{ xy(x²-y²) x²+y² (x, y) ± (0,0) (x, y) = (0,0) f(x, y) = %3D %3D ) Plot f(x, y). Where is f…

A: Given function is: fx,y=xyx2-y2x2+y2,x,y≠0,00                   ,x,y=0,0

Q: Contour map of f(x, y). Is fa positive or negative at B?

A: To check whether fx is positive or negative at B, draw a horizontal arrow at B towards the positive…

Q: At what points (x, y) in the plane are the functions continuous? ƒ(x, y) = sin (x + y)

A: fx, y=sinx+y.

Q: Find an analytic function f(z) = u(x,y) | iv(x, y) whcre u(x, y) = c²x cos(y) c²y sin(y). %3D %3D

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Q: Edit Find div F and curl F if F(x, y, z) = 13y*z'i – 11x°2°j – 5xy'k. div F= 0 curl F= k (-55 a' 2º…

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Q: Find an equation of the tangent plane to the surface at the given point. f(x, y) = Y, (1, 8, 8) 10…

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Q: 2.3 Assume that the relation z +x*y° + tanh (2xz + 6x°y² - 26) 65 + 37y defines y = - implicitly as…

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Q: Caculate Sin x JA メ R. the triangle in the bounded where R is by X - axies xy-plane and y = X そ × =…

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Q: Find the image of y = 1 under f(z) =1/z %3D %3D

A: Image of y=1 under f(z)=1/z

Q: What are the relative extrema of f (x, y) = x² + y? – 25 subject to y = +.

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Q: Sketch the surface given by the function. z= 9-x?-y? 2x -2 2x

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Q: Identify all extrema of the function f(x,y) = x³+y³-3x-12y+20 on the plane and characterize them.

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Q: Let f(x.y) = x° +y*. Find the slope of the line tangent to this surface at the point (- 1, - 1) and…

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Q: eck when the analytic function f(z) = sin z be a conformal mapping? %3D

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