A function F is defined on R2 by F(x,y) (picture)  let f(x,y)  = (x2y+2xy2) / (x2 + y2)  Determine F1(x,y) and F2(x,y) when (x,y) =/ (0,0)  (∂f/∂x and ∂f/∂y)

Q: exist. :) Compute the linearization of f(x, y) at the point (x, y) = (1,1). %3D

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Q: Find div F and curl F if F(x,y, z) = x°i – 11j + yzk. - div F= curl F=

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Q: Find the linearization L(x, y) of the f(x, y) = x°y® at the point (2, 2). L(x, y) = %3D

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Q: (a) Show that a differentiable function f decreases most rapidly at x in the direction opposite the…

A: if f is a differentiable function of x and y then function has directional derivative in the…

Q: (x, y) frx (x, y) fyy (x,y) f, (x,y) Point 1 1 Point 2 Point 3 -1 -1 -1 -1 1 Point 4 -1 -1 Point 5…

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Q: Find the directional derivative of f at the given point in the direction indicated by the angle θ.…

A: We have given f(x, y) = y cos(xy) at the point (0, 1) in the direction indicated by the angle θ =…

Q: [Find div(F x G) and Curl (F x G) where F(x, y, z) = x²yi + y³z²j – 2z²k | and G(x, y, z) = 3xyi –…

A: Given Fx,y,z=x2yi+y3z2j-2z2kGx,y,z=3xyi-5yzj+4z2k

Q: 4. Determine the directional derivative of f(r, y, z) = xe"+rsinz+a²y at the point (2,0, ) in the…

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Q: A surface S is described by the equation f(x, y, z) = n where f(x, y, z) = yz + nx²y+ yz³ (a) Find…

A: Given fx,y,z=yz+nx2y+yz3 Substitute n=5 Hence, fx,y,z=yz+5x2y+yz3 (a) We have to find the equation…

Q: Find the gradient of the function at the given point. Function Point f(x, y, z) = Vx2 + y2 + z2 (5,…

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Q: 21 (important) Find the fixed point for F(x) = ax + s. When is it attracting?

A: Given Fx=ax+s

Q: a) Find the directional derivative of f(x, y, z) = x²yz + 4xz² at (1, -2, 1) in the direction 2i - j…

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Q: Find div F and curl F if F(x, y, z) = x*i – 5j + yzk. - div F= curl F=

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Q: Find div F and curl F if F(x, y, z) = x°i – 9j + yzk. - div F= curl F=

A: Divergence of a vector function F(x,y,z) is given by, div(F)=i∂∂x+j∂∂y+k∂∂zF and curl of vector…

Q: (a) Find directional derivative and gradient of f(x, y, z) at indicated point. f(x, y, z)=, z-x u=…

A: To find the gradient of f(x,y,z), use the gradient formula,…

Q: Tangent to the curve z2 = 2xy + x2 , z = 3 , at the point ( 1, 4, 3) %3|

A: For a surface of the form: f(x, y, z)=0, the equation of the tangent at x0, y0, z0 is defined as…

Q: Find div F and curl F if F(x, y, z) = x°i – 6j + yzk. - div F= curl F=

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Q: Prove that the function ((z*)2 Iz| > 0 f (z) = z 0, z = 0 is not analytic at z = 0 by calculating…

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Q: The gradient of f(x, y) = e³ ª sin(4 · y) at (x, y) = (3, – 2) is defined as followed: V f(x, y) =…

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Q: Example Let f(r,y, z) = ryz sin rz. Find Vfo at the point Po = (1, –2, 7) and compute the…

A: to find : (1) grad f. (2) directional derivative.

Q: Find div F and curl F F(x,y,z)=x^2i-2j+yzk  F(x,y,z)=xz^3i+2y^4x^2j+5z^2yk

A: Given:- i) F(x,y,z)=x2i -2j+yzk   ii )F(x,y,z)=xz3 i+2y4x2j +5z2 yk To find:- div F and curl F of…

Q: Tangent to the curve z2 =2xy + x2, z= 3, at the point ( 1, 4,3

A: For a differentiable function, F(x,y,z)=0, the equation of a tangent line at x0,y0,z0 is given by…

Q: Find the gradient of the function at the given point. Function Point f(x, y, z) = Vx2 + y2 + z² (4,…

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Q: Find the gradient of the function at the given point. Function Point f(x, y, z) = Vx² + y2 + z2 (4,…

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Q: Find div F and curl F if F(x,y, z) = x°i – 5j + yzk. - div F= curl F=

A: A detailed solution is given below

Q: (a) Find the directional derivative of f(r, y, z) = 8ry2-+y at the point (1,1, 1) in the direction…

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Q: Find div F and curl F if F(x, y, z) = x'i – 3j + yzk. div F= curl F=

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Q: Find the gradient of the function at the given point. Function Point f(x, y, z) = x² + y2 + z2 (2,…

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Q: Find the gradient of the function at the given point. Function Point f(x, y, z) = Vx2 + y2 + z2 (2,…

A: We have to find maximum value of the directional derivative at the given point.

Q: (a) Show that a differentiable function f decreases most rapidly at x in the direction opposite the…

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Q: Find div F and curl F if F(x, Y, z) = x°i – 4j + yzk. div F= curl F=

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Q: Evaluate this function of z = cos x sin y; x = u – v, y= u² + v². Use chain - dz rule to find ди А.…

A: The given function are z=cosx siny; x=u-v, y=u2+v2.   Rewrite the given the function as follows.…

Q: Find the gradient of the function at the given point. Function Point f(x, y, z) = Vx² + y2 + z² (2,…

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Q: Find the directional derivative of the function at pointP in the direction of v. f(x, y, z) = y² +…

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Q: Find the directional derivative of F(x,y,z)=(xy^2)lnz at (1,2,e) in the direction of

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Q: Find the gradient of the function at the given point. Function Point f(x, y, z) = Vx2 + y2 + z² (7,…

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Q: Sketch the trace of f in the xz-plane. Find the directional derivative of f in the direction of the…

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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: Differentiate the function. y = In(In x) y' = %3D

A: Given y=ln(ln x)             y=ln(ln x).y'=ddx(ln (ln x))y'=1ln(x) . ddx(ln x)y'=1ln(x) . 1xy'=1x .…

Q: A surface S is described by the equation f(x, y, z) = n where f(x, y, z) = yz + nx²y+ yz³ 3 (a) Find…

A: Given f(x, y, z) = yz + nx2y + yz3 ∇fP⋅P=0 Now,…

Q: Find the gradient of the function at the given point. Function Point F(x, y, z) = Vx2 + y² +. (5, 4,…

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Q: A differentiable function f(x, y) has the property that f(1, 4) = 5 and f-(1, 4) = 3 and f,(1, 4) =…

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Q: (2) This exercise is to convince the student that the extension of the differentiation rules from…

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Q: Fundamental Theorem: Let f(x) = [ Jcos (In t)dt . Find the value of f'(æ). %3D

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Q: Explain why the function is differentiable at the given point. Then find the linearization L(x,y) of…

A: The given function is: f(x,y)=y+sinxyGiven point is:  P=(0, 3)

Q: Use Green's theorem to evaluate fxydx+ x3y3dy where C is a triangle with vertices (0,0), C (1, 0)…

A: Hey, since there are multiple questions posted, we will answer first question. If you want any…

Q: derivatives of u, v and w with respect to x, y and z, and use them to compute Jacobian Obtain the…

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Q: Find the gradient of the function at the given point. Function Point f(x, y, z)=√√√√x² + y² + z² (4,…

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Q: Find div F and curl F if F(x, y, z) = xªi – 2j + yzk. div F= curl F=

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Q: Find the gradient of the function at the given point. Function Point f(x, y, z) = Vx² + y² + z² (5,…

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