Q2: a) If W =F(x,y), where x =v -g and y = 2vg calculate W +W, b) What is the directional derivative of F(x,y,z)=(x+2y+3z) at point (1,-1,1) in the direction of -2i +2j -k

Q: Please show your answers to at least 4 decimal places. Suppose that f(x, y) = ry. The directional…

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Q: Suppose that f(r, y) ry. The directional derivative of f(x, y) in the directional (1, - 1) and at…

A: directional derivative f(x,y) = adf/dx +bdf/dy (a,b) = (1,-1) df/dx = y df/dy = x directional…

Q: Find the gradient of the function f(x, y, z) = xeyz, and the maximum value of the directional…

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Q: 1. The temperature at the point (r, y) on an unevenly heated plate is given by T = f(r, y) = 100+…

A: Given f=100+5x2+15x+10y2gradient of f∇f=∂f∂xi+∂f∂yj     =10x+15i+20yjAt (2, 1)∇f=10x+15i+20yj…

Q: If the gradient of f(x, y, z) at (1, 2, 3) is 2i – 2j +k, then the maximum value for a directional…

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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: Find the directional derivative of f(x, y, z) : 4y at P(3,1, –2) x + z in the direction from P to…

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Q: Let f(x, y, z) = 3xz + sin(ry)e*. what is faz? Find the gradient at the point (0, 0, 0)?

A: As per Bartleby answering guidelines if multiple questions are posted in a single picture then an…

Q: Please show your answer to at least 4 decimal places. Suppose that f(x, y) = ry. The directional…

A: Find the directional derivative of the function

Q: Find the maximal value of the directional derivative of w = xy°z at the point (2, 1, 1)

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Q: Let F(x,y,z)=3x2+3y2+4z2. For which unit vector 0 will the directional derivative D0F at  (12,12,12)…

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Q: Consider the function z = f(x, y) = x° + x² cos y What is the directional derivative at (1,0)) if…

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Q: Find the direction in which the maximum rate of change occurs for the function f(x, y) = 3x sin(zy)…

A: The maximum rate of change of a function f(x, y) at (a, b) occurs in the direction ∇f(a, b)  where…

Q: Let F(x, y, z) =2x2+3y2+4z2. For which unit vector 0 will the directional derivative DoF at…

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Q: 2y Find the directional derivative of f(x, y, z) = x + z at P(4,4, –3) in the direction from P to…

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Q: What is the linearization L(x, y) of a function f (x, y) at a point (a, b)? How is L(x, y) connected…

A: Linearization L(x,y) of a function f(x,y) is given by the formula

Q: The gradient vector for the surface xy + xz + yz = 1 at the point (1, 1,0) is (1, 1,0). Select one:…

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Q: Which direction is the directional derivative of the function f (x,y, z) = x2 – 2yz at point…

A: Solution: The function is fx,y,z=x2-2yz The point is P1,1,1 We have to find the direction in which…

Q: Find the directional derivative D,f(P) of f(x, y, z)= cosx+y+z°-5 at P:(, 1, 1) in the direction of…

A: Solved below

Q: Suppose that f(æ, y) f(x, y) in the directional (1, – 1) and at the point = xy. The directional…

A: Here, the given function is: f(x,y)=xy So, ∇f=∂f∂x,∂f∂y⇒∇f=y,x⇒∇f(4,-3)=-3,4

Q: Compute the directional derivative of f(r.y) = at the point (1, 1) in a direction normal to the…

A: Given that: f(x,y)=x2y at the point (1,1) Ellipse: x2+2y2=1 at the point (1,0)

Q: Compute the directional derivative of the function f(x,y, z) = 3ryz at the point P: (1, –3, –1) in…

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Q: Suppose that f(I,2) =3 and that the directional derivative of fat point (1,2) in the direction of…

A: Thr given problem is to estimate the value of f(1.1,2.1) with given values f(1,2)=3 and directional…

Q: 2. Prove that the directional derivative of f(x, y, 2) = ry sin z at (1,2, ) in the direction v = i+…

A: Given:        fx,y,z=xy sinz         x,y,z=1,2,π2    direction v=i+2j+2k   Differentiate the…

Q: #3. Consider the function xy2 if (x, y)# (0,0), f (x, y) = {x2+y2 if (x, y) = (0,0). Calculate the…

A: Given function is fx,y=xy2x2+y2if x,y≠0,00          if x,y=0,0 We have to calculate the directional…

Q: 3. At point (1,0,3) on the surface f(x,y) = 2x^2 + 3 y^2+ z^2-11, the directional derivative in the…

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Q: Find the directional derivative of F(x , y , z)=7y2e−x+3z2 in the direction u=(3,6,−2) at the point…

A: We have to solve

Q: 2 - What is the directional derivative of the function f(x,y,z) = x3 - 2xy +z at point Ao= (1,1,0)…

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Q: Find the directional derivative of f(x, y, z) = xz + y°, at (3, 2, 1) in the direction of 3 = 1+3+…

A: We need to find gradient of f at point (3,2,1)

Q: Let f(x, y, z) = 3xy + 2yz - xz. Find the directional derivative of f(x, y, z) in the direction of…

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Q: Compute the directional derivative of f (x,y)= at the point (1,1) in a direction normal to the…

A: The directinal derivative is given below

Q: 4. Compute the directional derivative of f(r, y) = at the point (1, 1) in a direction normal to the…

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Q: If f(x,y) = ln(xy) + x^2y^2, how do I calculate the second directional derivative of f in the…

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Q: 5. Compute the directional derivative and gradient of f(x,y,z) = 4x – y²e3xz at (2. –1.0) in the…

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Q: a) If W = F(x ,y),where x =v²-g and y 2vg calculate W +W, %3D b) What is the directional derivative…

A: W=f(x,y) and x= v2-g2 & y=2vg   Wx = dW/dx = (df/dx*dx/dv) + (df/dx*dx/dg) ..............From…

Q: What is the rate of change of the function f(x,y) = ye^(2cos x) + tan(x+3y) at ( 3π/2 , π/2) in the…

A: Given: fx,y=ye2cosx+tanx+3y To Find: Rate of change of fx,y in the direction of the vector 3,4 at…

Q: Suppose that f(z, y) = z*y°. The directional derivative of f(1, y) in the directional ( – 1, – 2)…

A: We can solve this as follows:

Q: Find the gradient of the function and the maximum value of the directional derivative at the point…

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Q: Compute for the directional derivative of f (x, y, z) = tan (Tx – 21ny)e4y-z at the point (, 0, In…

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Q: Find the unit vector u along which the rate of change of the function f(x, y) = x 2 + xy3 at the…

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Q: 8y If the directional derivative of f(x,y)D at (2,1) in the direction of (a, 2) is equal to zero,…

A: Given,            f(x,y)=8yx

Q: ) Compute the directional derivative of f(x, y) = x2 y at the point (1, 1) in a direction normal to…

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Q: 8. Find the directional derivative of f (x, y, z) = xy²z³ at P(2,1,1) in the direction of Q(0, –3,5)

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Q: Find the directional derivative of f(x, y, z) = xy²z³ at P(4, 1, 1) in the direction of Q(0, –7, 9).…

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Q: 2. Find the directional derivative of f(x, y, z) = y – Væ² + z² at P(-3,1,4) in the direction of a =…

A: Given f(x,y,z)=y-x2+z2

Q: Find the directional derivative of f(x,y)=sin(2x−2y) at the point (π/2,π/6)in the direction of the…

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Q: Use the definition of directional derivative to solve Duf(xo, yo, zo) at point P(xo, yozo) where…

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: What is the directional derivative of f(x,y,z) = ln(x²+2y²+ 4z²) at the point P(-1, 2, 4) in the…

A: The given function is; f(x,y,z)=ln(x2+2y2+4z2) Point P(-1,2,4) u=-3i/13 -4j/13 -12k/13.

Q: Find the work done by the gradient of ƒ(x, y) = (x + y)2 counterclockwise around the circle x2 + y2…

A:

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.