Problem 19 through Prob. 21 are based on the following statement. A two-dimensional function, (r, y), is defined as f(z.v) = 2-+ 3x- y 19. What is the gradient vector for this function? (A) V/(E,) = (2 + 32)i+(- - 9i (B) V/(r, y) = ( +i+(-- (C) V/(r, y) = (4z+3)i+(-2y-1)j (D) V/(z y) = (3r + 4)i – (2y + 1)j %3D 20. What is the direction of the line passing through the point (1,-2) that has the maximum slope? (A) 41+2j (B) 71+3j- (C) 71+4j (D) 91-7) 21. What is the magnitude of the slope at the point 0.-2)? (A 2.1 (B)3.5 (C) 7.6 (D87

Q: If g(x, y) = x² + y² 6x, find the gradient vector Vg(1, 6). Vg(1, 6) = -4,12 Use the gradient vector…

A: Given that , gx,y=x2+y2-6x find the gradient vector ∇g1,6 and tangent line to the level curve…

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Q: 15) Suppose z is implicitly given by the equation x³y – yz2 += 4 in a neighborhood of the point X P…

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Q: Question 4 Find the gradient of the function at the given point. w = 2x - 4yz+z², (1, 1, −2) 21+…

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Q: 2. Find the directional derivative of o = yx2 +x²z + 3xyz in the direction of vector n = î + 2 ŷ -2·

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Q: Given that the directional derivative of f at the point (1, –6, 1) in the direction of a = 2i – j–…

A: We have to find the gradient of f at point (1,-6,1).

Q: 5. If the gradient of f(r, y) at (1,2) is 2i – 2j, then the maximum and minimum values for a…

A: As per honor code, we are entitled to solve only 1 question at a time so I am providing you the…

Q: QUESTION 9 Letf(x yz) be a function with the gradient vector . What are the extreme points off with…

A: Given: ∇f=<2, 6, 12>g=x2+y2+z2=46  We solve it by method of Lagrange multipliers ∇f=λ∇gg=k

Q: Find the gradient of the function at the given point. In(x2 - Y) - 9, (3, 8) Vz(3, 8) =

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Q: Problem 1. Find the directional derivative of f(r, y) = sin(x + 2y) at the point (3, 1) in the…

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Q: Question 1 Consider the function f with f(x,y) = x + y. Use the Lagrange multiplier method to show…

A: Given: f(x, y)= x^2 + y^2

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Q: For an equation x" +x = 0 a) Draw a tangent vector to a solution (x(1), x' (1)) in the phase plane…

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Q: 35. Give linearly independent functions that are annihilated by D² (D² – 2D + 10).

A: We will find roots for the equation and use concept of differential equations to find the linearly…

Q: The present problem focuses on the function v defined by Equation (1): 1 1 v(x, y) = x² + y?+ (1)…

A: Given,  v(x,y)=x2+y2+1(x-12)2+y2+1(x+12)2+y2 To find the stationary points while x=0.

Q: Problem 1.11 Find the gradients of the following functions (a) f(x, y, z) = x² +y³ +z*.

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Q: Example 4 Find the directional derivative off(x. y. z) = xy -v+at the point (1,-2,0) in the…

A: If f is differentiable at x,y,z  , then f has a directional derivative in the direction of any…

Q: 2. Find the gradient vector at the indicated point f(x, у, 2) 3 ху — In (2),. (2, -2,2)

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Q: Find the gradient of the function at the given point. In(x² – y) - 9, (3, 8) z = Vz(3, 8) =

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Q: problem (A), find a linear approximation f(x, y) at the indicated point. [3x – y² A) f(x,y) = at…

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Q: Let f(xv) = 2x3 – 4xy + yt. Give detailed explanations for your answers to the %3D following. (a)…

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Q: Find the directional derivative of f(x,y,z)=4x^2y-7z^3x+y^2 at the point (2,1,-1) in the direction…

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Q: Work problem 3 Given the vector function () 5 F(t) = (6t³ · (61³ – —‚ t - sec(4 – t)), then find the…

A: We have to find the tangent vector at t=4.

Q: EXAMPLE 4 Find the directional derivative of the function f(x, y) = x²y³ - 5y at the point (2, –1)…

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Q: The gradient vector of the function f(x, y) = sin(4x - 6y) is (4 cos(4x - 6y), 6 cos(4x - 6y)).…

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Q: (10) Suppose that below are several level curves of f(x, y). Draw vectors that represent the…

A: Given: The vector field ∇ f whose value at a point p is the vector whose components are the partial…

Q: 7

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Q: Suppose z is given implicitly by the equation ln (yz2) + x3z = −1 in a neighborhood of the point P…

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Q: Suppose z is implicitly given by the equation x³y-yz²+ -5 x In a neighborhood of the point P(1, 1),…

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Q: QUESTION 9 Le tf(x, y.z) be a function with the gradient vector . What are the extreme points of f…

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Q: The gradient vector of the function f(x, y) = ln(xy) — x³ at the point (-1, 1) is (-1,-2). Select…

A: This question is based on gradient of function at a point.

Q: Question 10. Find the gradient of the curve f(2) = -2³ + 10z? – 3 at z = 4. Gradient =

A: Let's find.

Q: QUESTION 6 The gradient of z= 4x-8y is O vz=4i-8j O Vz=8i-4j O vz= -4k O Vz=4i+8j

A: Given that, z=4x-8y To find gradient of z. Use formula, ∇z=dzdxi^+dzdyj^

Q: (х,у,2) xIny + ylnz + zlnx

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Q: Le tf ( x, y ,z ) be a function with the gradient vector . What are the extreme points of f with…

A: Let gx, y, z=x2+y2+z2 The gradient value of f and g are                  ∇fx, y, z=2, 6, 12∇gx, y,…

Q: 1. Find the Gradient of the following a. F, = x'e" - y': b. F, = 4x' - 3y +5=?

A: Solution is given as below:

Q: This question is based on Activity 2.7.2 of Active Calculus. 3 -3 3 -3 Find an equation of the line…

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Q: QUESTION 3 Compute the gradient of the function at the given point. Q13: f(x y) = ln(9x - Sy), (-10,…

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Q: Suppose z is given implicitly by the equation x3y-yz2+z/x=4 in a neighborhood of the point P (1,…

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Q: Question 3 a. Find the gradient of r=x +y² + z?

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Q: In problem2 , find a vector in whose direction f(x,y,z) has zero change (zero derivative) at point…

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Q: Find the gradient of the function at the given point. In(x² - y) - 9, (2, 3) = Z Vz(2, 3) =

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Q: (a) Suppose that the changes in power a and drag y are small. Use the linear approximation of f to…

A: Given: v(P,C)=2PkC13 The corresponding fractional change in speed is given as,…

Q: Le tf ( x, y ,z ) be a function with the gradient vector . What are the extreme points of f with…

A: This is a problem of function of several variable We have to find the extreme point in three…

Q: Problem 12.2. The function f(x,y,a,b) is f (x,y,a,b) = a²x + xy² + y³ 1 + x² + y² + 1 + a? + by, 33…

A: Solution: The function is fx,y,a,b=a2x+xy2+13y3+x2+y2+12b2+a2+by (a) The gradient of fx,y,a,b: Here,…

Q: If ø = 3r²y – y³,2. Find gradient Vø at the point (1, –2, –1).

A: The solution is given as

Q: 8 3 D is a curve that is represented by the vector function H(t) = - A. Given x(t) e2t , determine…

A: NOTE: Refresh your page if you can't see any equations. .

Q: 6. Suppose that the temperature T at point (x, y,z) is given by the function T = 2x2 – y? + 4z², and…

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Q: Work problem 30 Given the vector function 5 F(1) = (61³ – ¾, sec(4 − 1)), t then find the tangent…

A: Given :Ft=<6t3-5t, sec4-t>at t=4