8. Consider the function f(r, y) = 4+6x² +3y². which is differentiable in an environment D from the point P (-4, -1). The value of the directional derivative of f at P in the direction of the vector u = (-5, -4) corresponds to 216 A) 41 264 B) 41 216 V41 264 D) 41

Q: Find the point on the graph of z = 3x2 + 2y at which vector (24, 8, 2) is normal to the tangent…

A:

Q: Consider the curve y = 10 + 4x − x^(2) at (x, y) = (3, 13). Find a vector, v, that has length 4 and…

A: Given the curve y=10+4x-x2 at (x,y)=(3,13).

Q: Find a vector tangent to the curve of intersection of the surfaces given by x² + y² + z² = 1 and 2²…

A:

Q: Find the ar ea of sur face x - 2y - 2z = 0 that lies above the triangle bounded by the lines x = 2,…

A: Given :          The surface x2 - 2y - 2z = 0 that lies above the triangle bounded by the lines x…

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

A: Given that f1,2=3 and the directional derivative of f at point (1,2) in the direction of the vector…

Q: Find the directional derivative of f(r, y, z) = yr + z* at the point (2, 3, 1) in the direction of a…

A: Directional Derivative of a Function of Three Variables =>Directional derivative of  f ( x , y ,…

Q: 1. Given the time_Varying position Vector X iat+j bf2+Kct 3 where ast,b=2,andc=3_are Cnstants. Find…

A: SOLUTION-

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

A:

Q: Suppose given a function f(x, y, 2) of three variables, and a point (o, y0, 20) €R. Explain in your…

A:

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

A:

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

A: Given : f1,2=3 and the directional derivative of f at 1,2 in the direction of the vector i+j is…

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

A:

Q: Find the directional derivative of f(x, y, z) (2,1,3) in the direction of a vector making an angle…

A: Given the function f(x,y,z)=zx+y4

Q: 1. Find a vector which is tangent to the curve of intersection of the surfaces z = x2 – y? and xyz +…

A:

Q: Find the directional derivative of f at P in the direction of a vector making the counterclockwise…

A:

Q: 1. Given the time_Varying position Vector x iat+jbt2+Kct z where ast,b=2,andc=3_are Gnstants. hind…

A: Given : a=1, b=2, c=3 x = iat+jbt2+kct3

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

A:

Q: Suppose ƒ is differentiable at (9, 9), ∇ƒ(9, 9) = ⟨3, 1⟩, and w = (1, -1). Compute the directional…

A: Given that ∇ƒ(9, 9) = ⟨3, 1⟩. Note that w = (1, -1) is not a unit vector. Its unit vector along same…

Q: Find the work done by the force F- Tyi + (y - ±)j over the straight line from (0,0) to (3,6).

A:

Q: 2. Prove that the directional derivative of f (x, y, z) = xy sin z at direction v = i+2j+ 2k is .…

A:

Q: Find the direction in which the maximum rate of change occurs for the function f(z,9)2zsin(ay) at…

A:

Q: Represent the plane curve by a vector-valued function. 2x − 3y + 5 = 0

A: Given: 2x-3y+5=0 for finding given equation in vector form, we assume x=t and find value of y in…

Q: Let f(x, y, 2) = cos(ryz) Find the directional derivative of f at the point (,, 7) in the (a)…

A: We have to find Directional Derivative and Largest possible value.

Q: Find equations of the normal line and the tangent plane to the parametric surface defined by the…

A: NOTE: Refresh your page if you can't see any equations. . the given point is  compare coordinate on…

Q: Let f(x,y)= e, Compute the cartesian equation of the tangent plane r,y) at the point (2.2).

A: The equation of tangent plane

Q: In what direction from the point (1,-1) is the instantaneous rate of change of 22 f(x,y) = 3x* –…

A:

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: 22 Find the Directional Derivabive of Pary,z)= xg-y2'+Z at the point CI, -2, 0) in the direcbion of…

A:

Q: Find the directional derivative of the function f(x, y, z) = /ryz at the point P(2,2, 2) in the…

A: Topic-vector calculas

Q: The position of a particle moving in the xy-plane is given by the vector (4t, y(2t)), where y is a…

A:

Q: a) What is the rate of change of f(x, y) = 3xy + y^2  at the point (2, 4) in the direction of vector…

A: (a) Given Data: Function: f(x, y)=3xy+y2 Point: (x, y)=(2, 4) Direction of vector: v=-3i-j The…

Q: Given the function of two variables ƒ(x, y) = 4x³ − 60x² + 12xy² − 24y² +3. - - Find and classify…

A:

Q: The directional derivative of xy f(x, y) = x + y) at (1, 1) in the direction of the unit vector at…

A:

Q: Find a vector equation for the curve of intersection of the surfaces x^2 + y^2 = 4 and z = xy.

A:

Q: (#2) Evaluate the directional derivative Duf (3, 4) if f (x,y) = Vx² + y² and u is the unit vector…

A: The expression for the directional derivative of the function f in the direction of u at a point…

Q: Compute the unit binormal vector and torsion of the curve. r(t) = (10t, 3 cost, 3 sin t) (3, 10…

A:

Q: Let f(x,y,z)=xyz. What is the directional derivative of f in the direction of the unit vector…

A:

Q: 11. Calculate the directional derivative of the function f(, y, z) = xyz at the point a (-1,0,2) in…

A: See the answer below

Q: Find a nonzero vector normal to the plane z − 5(x − 1) = −2(3 — y). - -

A:

Q: The directional derivative of xy f(x, y) = V2 (x + y) at (1, 1) in the direction of the unit vector…

A: We have ,  f(x , y) = xy2x + y   We know that , directional derivative at any point x , y is defined…

Q: Find the directional derivative Duf(1, 1), where f(x, y) = x2 + y2 and u is the unit vector at an…

A:

Q: Prove that the vector T'(t) = 0 for moving in a straight line

A: Note that, the object's path is rt=xti+ytj. yt=mxt+b, where m and b are constant. It is known that,…

Q: Compute the directional derivative and gradient of f(x, y, z) = 4r – yez at (2, -1,0) in the…

A: Given: fx,y,z=4x-y2e3xz       at     2,-1,0 Directional Derivative = Gradient of function x unit…

Q: a. Find the direction in which the directional derivative of f(x,y), at the point (z, y) = (0,4),…

A:

Q: Find a vector tangent to the curve of intersection of the two cyclinders x2 +y? = 200 and y? + z2 =…

A:

Q: 2. Compute the vector line integral: -y х — 4 Le (x – 4)² + y² dx + (x – 4)2 + y² dy where C is the…

A:

Q: Let F(x, y, z) = 5x² + 2y2 + 522. For which unit vector 0 will the directional derivative DoF at (2,…

A:

Q: 10. Find the work done by the force F=vx +2y y - 7 for a particle that moves between points (-1,0,1)…

A:

Q: Prove that the directional derivative of flay.2) = aysinz. direction v=i +2j+2k 1Is Sin Z at…

A:

Q: Let f ( x , y ) = 2 x − y + x2 + y4. Which (unit) direction vector u  MINIMIZES the directional…

A: