2. Calculate the directional derivative of the scalar field U(x, y,z) at the point M,, along the direction of a normal vector to the surface S, that makes an acute angle with Oz axis, if U y 1%3 y, S:x-y-z+12=0, M(2; 2; 4).

Q: Find the directional derivative of the scalar field ¢ = xªy + 3xz at the point (1, −1, 4) along the…

A:

Q: 3. Calculate the directional derivative of the function f : R³ → R, defined by f(x, y, z) = y²+xz at…

A: Step 1: Step 2: Step 3: Step 4:

Q: Find the directional derivative of the function at the given point in the direction of vector v.…

A: the vector field is  g(x,y,z)=(x+4y+3z)32  point (2,1,1) to find the directional derivative in the…

Q: Find the directional derivative of the scalar field = x³y + 4xz at the point (1,-1, 2) along the…

A:

Q: 4. Let r(f) = ° 13 i - 6fj + Pk. (a) Find the unit tangent vector T(t) and T(3). | (b) Find the…

A:

Q: Find the directional derivative Du f(−5/6,1) for the function f(x,y)=cos(π(3x+4y)) in the direction…

A: It is given that fx,y=cosπ3x+4y. The objective is to evaluate the directional derivative Duf-56,1…

Q: 1) For f(x, y,z) = x2 – (1 – y)? + z?. Find directional derivative of f at P(1, 1, 1) in the…

A: Given that  f(x,y,z)=x^2-(1-y)^2+z^2 Point P(1,1,1) Vector is a=(0,3,4)  To find the directional…

Q: If the percent decrease is 25%, what is the common ratio?

A: Common Ratio The common ratio is defined as the amount between each number in a geometric sequence.…

Q: 1. Let R and b be positive constants. The vector function r(t) = (R cost, R sint, bt) traces out a…

A:

Q: Determine the directional derivative of the following functions in the vector direction specified at…

A: Here we will find out the required value.

Q: 5. Compute the directional derivative and gradient of f(x, y, z) = 4x – y²e3xz at (2, – 1, 0) in the…

A: Gradient of vector function For a given vector f(x, y, z) the gradient vector denoted by ∇(f) is […

Q: Determine the directional derivative of the following functions in the vector direction specified at…

A:

Q: Find the directional derivative of the function f(x, y) = 2x2y + 6xy at (1, 1) in the direction of a…

A:

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

A:

Q: Let F(x,y, z) = rye" – 2² Jī and P(1,0, –1).

A: Given Fx,y,z=xyey-z2x and P1,0,-1Vector u=⟨2,-3,6⟩

Q: 1. Consider the function z= f (x, y). a. Give the formula for the gradient at P= (a, b). b. Give the…

A: Consider the given information.   (a) The given function is z=f(x,y) and the point is P=(a,b).…

Q: 2. Consider a function g(x, y, z) = 1 + ln(3x + 6y +9z) and a vector u = (0, -1, 1). (a) Find the…

A:

Q: Find the directional derivative of the function f(x, y, z) = xe³ + ye² + zeª at the point (0, 0, 0)…

A: The given function is:f(x,y,z)=xey+yez+zex

Q: Let P be the point (2, -1, 2) and Ø,: x² + y² – z² = 10. (i) Find the unit normal vector to the…

A: (c) The given surface is ∅1: x2+y2-z2=10 and the point P: 2,-1,2. (i) The unit normal vector to the…

Q: Let f(x,y)=y2 +sin(y+T)+x +cos(xe). At the point (TT,0) compute the unit vector in the direction of…

A: We have to find the unit vector in the direction of the maximum increase of the function f. This…

Q: Find the directional derivative Duf (2,0) where, f(x, y) = xexy + y and u is the unit vector in the…

A:

Q: Consider the function f(x. y. =) = 1 /g² + =². (a Find the gradient vector Vf. Write your final…

A:

Q: 1. Find the directional derivative of the function f(x,y) = e* seny at the point ((0,π/3), in the…

A: Step 1: Step 2: Step 3:

Q: a) Find the directional derivative f (x, y, z) = x In(y+z) at point P (2, e, e) in the direction of…

A: We have to find directional derivative of vector f in the direction of vector v:

Q: Find the directional derivative Du f(P) of f(x, y) = x" at the point P(1,2) in the direction of the…

A: Given that       f(x,y) = xy at the point P(1,2) in the direction of the vector v = (2,-1). Here we…