Find the linear approximation of the function f (x, y, z) (3, 2, 6) and use it to approximate the number /(3.02)² + (1.97)² + (5.99)². Va² + y² + z² at

Q: (a) Find the points (x ,y, z) in space, where the function f(x, y, z) = Vx² +y -1 Is continuous.

A: It is well known that the equation z=x2+y2 represents a circle with centre at the origin. The…

Q: Use the linear approximation to f (x, y) = √x/y at (9, 4) to estimate √9.1/3.9.

A: f(x,y)=xy at (9,4) to estimate 9.13.9

Q: Find the linearization L(x, y) of f(x, y) = x2 y3 at (a, b) = (2, 1). Use it to estimate f(2.01,…

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Q: Let f(x, y) = . Use the Linear Approximation at an appropriate point (a, b) to estimate…

A: Given,f(x,y) = x2y2+1To estimate,f(4.02,0.93) using the LinearApproximation at an appropriate point…

Q: 2. Find a function f(r, y, 2) which makes (yz?, rz?, f(r, y, z)) conservative. Show that your answer…

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Q: Use the linear approximation of f(x) = at r = 0 to approximate f(-0.1). 1+r

A: Use the linear approximation of f(x)=1/(1+x) at x=0 to approximate f(-0.1).

Q: Find the linear approximation to the equation f(x, y) = 3, zy at the point (6,2,6), and use it to…

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Q: Find the linear approximation of the tunction fox) = NT-x at a-0 %3D and use it to approximate the…

A: We find f'(x) using the power rule.   then we find f(0) and f'(0)

Q: Find the linear approximation of the function f(x, y, z)=√√x² + y² + z² at (9, 6, 2) and use it to…

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Q: Let f(x, y) = x2 /(y2 + 1). Use the Linear Approximation at an appropriate point (a, b) to estimate…

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Q: Find the linear approximation to the equation xy f(x, y) 2. at the point (4,6,4), and use it to…

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Q: Find the linear approximation of the function f(x, y, z) =  sqrt x2 + y2 + z2 at (6, 6, 7) and use…

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Q: Find the linear approximation of given function at (0, 0). 3x + 4 2y + 1 f (x, y) = f(x, y) =

A: We have to find the Linear approximation of the given function.

Q: Use the Linear Approximation to f(x, y) = x/y at (9, 4) to estimate 9.1/3.9.

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Q: The linear approximation at x and where B is:

A: Given a trigonometric functionf(x)=sin(6x)

Q: Find the linear approximation to the equation f(x, y) = 2, at the point (4,2,4), and use it to 2 %3D…

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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: Find the linearization of the function f (z) =23 at z = 1. L(z) = Using this linearlization, f…

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Q: Find the linearization of the function f(x, y) 155 – 2x2 – 5y² at the point (5, 4). L(x, y) = Use…

A: Given:      f(x,y) = √ (155 - 2x2 - 5y2 )     Point : ( 5 , 4 )  Now     Linear approximation f (…

Q: Find the linear approximation of the function f (x, y,z)= x' Vy +z° at the point (2, 3, 4) and use…

A: Given:-               Find the linear approximation function f (x,y,z)= x 3y2+z2 at the point…

Q: Let f(x, y) = Use the Linear Approximation at an appropriate point (a, b) to estimate f(4.04, 0.94).…

A: Given that  f(x,y)=x^2/(y^2+1) From the linear approximation to find the f(4.04,0.94)

Q: Find the gradient of the function f(r, h) = 2xrh + xr² at the point (2, 2). V f(2, 2) =

A: Given,   f(r,h)=2πrh+πr2

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 linear approximation of the function f(x, y, z)=√x² + y² + z² at (4, 7, 4) and use it to…

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Q: Using the linear approximation of f (x, y) near (x, y) = (1, 0) tells us that f (0.98, 0.05) is…

A: The linear approximation of a function f(x, y) at (a, b) is L(x, y) = f(a, b) + fx(a, b)(x − a) +…

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: Find the gradient of the function: f(x, y, z) = x'y + = OF = (7x + 6x°)i + 3y²j + k %3D OF = 7x°y°i…

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Q: e) Find the linear approximation of the function f(x, y, z) = x³y² + z² at the point (2, 3, 4) and…

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Q: Find the local linear approximations L to the specified function f (x, y)= xsiny at the point P…

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Q: Let f(x) = x“.4x3 Find the derivatine of P (x) and the points, (X,y), where te tingent line is…

A: f(x) = x4 - 4x3f'(x)=ddx(x4 - 4x3)f'(x) =4x3 - 12x2

Q: Find the linear approximation of the function f(x, y, z) =    x2 + y2 + z2 at (4, 8, 8) and use it…

A: Solution is given below:

Q: Find the differential of f(x, y) = Vr2 + y³ at the point (2, 3). df = Then use the differential to…

A: given function is f(x,y) =x2+y3 we know, for the function z = f(x,y), the total differential of the…

Q: Let f(x, y, z) = xyz Find the direction in which the function increase most rapidly at the point…

A: Given: fx,y,z=xy2z3 The gradient of a function if given by ∇f(x,y,z) =∂f∂x,∂f∂y,∂f∂z.

Q: Find the linear approximation to f (x, y, z) = 3, -3, – 1): at the point | F(x, y, z) ×

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Q: Find the linearization of f (x, y, z) = xy / z centered at (2, 1, 2). Use itto estimate f(2.05, 0.9,…

A: Our Aim is to find the linearization of f(x,y,z) =xyz centred at (2,1,2).and then using that value…

Q: Find the linearization of the function f () = z7 at z = 1. L (z) = 固助 Using this linearlization, f…

A: Given function is

Q: Let f(x, y) = 2x^3+5y. Find the linear approximation of f(x, y) near (1,5), and use it to estimate…

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Q: Integrate f(x,y,z) = x-3y + z over the line segment joining the points (0,0,0) and (2,2,2). %3D

A: Here, we need to integrate f(x, y, z)=x-3y2+z over the line segment joining the points (0, 0, 0) to…

Q: Find the linear approximation of the function f(x)= cuberoot(1+x) centered at 0. Use this to…

A: For the solution follow the next step.

Q: Find the linear approximation to f(x, y) f(6.11, 4.17) f(6.11, 4.17) = 5, xy at the point (6, 4,…

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Q: Find the linear approximation of the function at the give f(x.y) = 3x y at (- 6,9) O A. L(x,y) = -…

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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 of the function f(x, y, z) = V x² + y² + z² at (3, 6, 2) and use it to…

A: Given: f(x,y,z)=x2+y2+z2 at (3,6,2)find f(3.01,5.98,1.97)=3.012+5.982+1.972

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: use linear approximation to give an estimate for the value of g (0.97, 2.01, 3.02) given g (x, y, z)…

A: Linear approximation of a function : The linear approximation of a function f(x,y,z) at some point…

Q: Find the linear approximation of the function f(x, y, z) = Vx2 + y? + z? at (2, 9, 6) and use it to…

A: The linear approximation of a function f(x, y, z) at (a, b, c) is L(x, y, z) = f(a, b, c) + fx(a, b,…

Q: Use the Chain Rule to find dQ where Q=√√3x² + 3y² + 4z², x= sint, y = cost, and z= cost. dt'

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Q: Find the image of the line z =3 +iy under f(z) = e

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Q: Find the linearization of f (x) = xe¯* at a = 0. (Hint: Remember thne product rule.)

A: Given : fx = xe-x2

Q: Use the linear approximation to ƒ(x, y) 12x² at (3, 9) to estimate f(3.1, 8.8). y2+7 (Use decimal…

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