Calculate the directional derivative of f(x,y,z)=x(y^2)+y((1-z)^(1/2)) at the point P(1,−2,0) in the direction of the vector...

Calculate the directional derivative of f(x,y,z)=x(y^2)+y((1-z)^(1/2)) at the point P(1,−2,0) in the direction of the vector v = 5i+2j−k. (a) Calculate the directional derivative of f at the point P in the direction of v. (b) Find the unit vector that points in the same direction as the max rate of change for f at the point P.

Expert Solution

milcah answered 2 years ago

The directional derivative of a function F(x,y) at a point P (1,-3) in the direction of...

The directional derivative of a function F(x,y) at a point P (1,-3) in the direction of the unit vector - 3/5 i + 4/5 j is equal to - 4 while its directional derivative at P in the direction of the unit vector (1/root5) i + (2/root5) j is equal to 0. Find the directional derivative of F(x,y ) at P in the direction from P(1,-3) towards the point Q(5,0).

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Let F(x, y, z)=2xy^2 +2yz^2 +2x^2z. (a) Find the directional derivative of F at the point...

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Compute the directional derivative of T(x,y,z)=200e^(-x^2-3y^2-9z^2) at the point (2,-1,2) in the direction toward the point (3,-3,3). What is the maximum rate of change of T at the point (2,-1,2)? I have solve this by mathematica...

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1. For z=x^2-xy^2 find: a. the gradient for z; b. the directional derivative in direction of...

1. For z=x^2-xy^2 find: a. the gradient for z; b. the directional derivative in direction of <3,-1>; c.the approximation for Δz when taking a Δs =0.05 step from (1,2) in direction of <3,-1>; d. the approximation to the maximum Δz possible when taking a Δs =0.05 step from (1,2).

Find the directional derivative of f at the given point in the direction indicated by the...

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Given f(x,y) =(x3y- 2x2y) a) find the directional derivative of f(x,y) at (1, 2) in the...

Given f(x,y) =(x3y- 2x2y) a) find the directional derivative of f(x,y) at (1, 2) in the direction of <-3,4> b)find the maximum value of directional derivative at (2,4) and the direction in which this occurs

Compute the derivative of the given vector field F. Evaluate the line integral of F(x,y,z) = (y+z+yz , x+z+xz , x+y+xy )

Compute the derivative of the given vector field F. Evaluate the line integral of F(x,y,z) = (y+z+yz , x+z+xz , x+y+xy )over the path C consisting of line segments joining (1,1,1) to (1,1,2), (1, 1, 2) to (1, 3, 2), and (1, 3, 2) to (4, 3, 2) in 3 different ways, along the given path, along the line from (1,1,1) to (4,3,2), and finally by finding an anti-derivative, f, for F.

A) Find the directional derivative of the function at the given point in the direction of...

A) Find the directional derivative of the function at the given point in the direction of vector v. f(x, y) = 5 + 6x√y, (5, 4), v = <8, -6> Duf(5, 4) = B) Find the directional derivative, Duf, of the function at the given point in the direction of vector v. f(x, y) =ln(x2+y2), (4, 5), v = <-5, 4> Duf(4, 5) = C) Find the maximum rate of change of f at the given point and the direction...

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