Find the linearization L(x,y) of the function f(x,y) = x - 5xy + 2 at Po(5,2). Then find an upper bound for the magnitude |E| of the error in the approximation f(x,y) = L(x,y) over the rectangle R: |x-5|s0.5, ly-2|s0.5.

Q: Consider the function f(x, y) = In(x² + y² + 1). 2 (a) Find Vf(1, 2). (b) Find Daf(1, 2) in the…

A: f(x,y)=ln(x2+y2+1) (a)Gradient vector…

Q: Let f(x, y, z) = 5x³ - y³ + z². Find the maximum value M for the directional derivative at the point…

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Q: Find (url and dive rgence the of F(xy2)=Xy2 i+ 2x Y j t z(os xyk.

A: Given: F(x, y, z) = xyz i + 2xy j + 2cosxy k To find: Curl and divergence of the given function.

Q: Find the linearization of the function f(x,y) = V9x² + 16y² at the point (1, 1), and use it to…

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Q: Find the linear approximation of the function at the given point. f(x, y) = 4 sinx - 6 cos y at (0,-

A: Given,           The function fx,y=4sinx-6cosy  at  0,π2.

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: ƒ(x, y) = x¹y — x²y³

A: Please see the below picture for detailed solution.

Q: Find the directional derivative of f (x, y) = -3 yx³ + xy² set by the line r(t)=(-2+ 2t,√5t). at the…

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Q: Find an equation of the tangent plane at the given point. f (x, y) = x/√y,  (4, 4)

A: Given : The function is f ( x, y) = xy and point ( 4, 4 ).

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: Write the Linear Approximation to f(x, y) = x(1 + y)-¹ at (a, b) = (8, 1) in the form f(a+h,b+k)…

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Q: The directional derivative of f(x, y) = √5x + 3y at the point (4,3) in the direction corresponding…

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Q: The function f(x, y) = ¿e=y – In(y²)

A: It is partial derivative

Q: Find the derivative of the dot product (u(t) • v(t)) if u(t) and v(t) equal the following (see image…

A: Given vectors are we are to find the derivative of u(t).v(t)

Q: f(x, y, z) = x + tan(yz) exyz + 1

A:

Q: Find the linear approximation of the function at the given point: f(x, y) = 2 sin x – 3 cos y at (0,…

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Q: Calculate the rectangular approximations R1, R2, and R4 for f(x)=2x−1 over the interval [1,5].

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Q: Let 7(t) = (- 5t + 2, t² – 4t³, 3tª). Find the line (L) tangent to 7(t) at the point (7, 5, 3) L:(x,…

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Q: Consider f(x, y) = xy(²-x²) x² + y² 0 if (x, y) = (0,0) if (x, y) = (0,0) . Show that fay(0,0) = 1…

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Q: The graph of y=x'-3x-24x +32 is concave upward on the interval (1, oo) because: O'=y"=0 Oy' is…

A: The given function is y=x3-3x2-24x+32

Q: Find the linear approximation of the function at the given point. f(x, y) = 10x2-4y2 +8 at (5,6)…

A: fx,y=10x2-4y2+8 To find the linear approximation of the function at the given point at (5,6)

Q: Find the linearization of the function f (x) = a° at a = 1.

A: