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: 5. Find the directional derivative of f(x, y) = xy – y at the point (1, 2) along the unit vector…

A: The given function is: f(x,y)=xy-y2 Given point is: P = (1, 2) Direction vector is: v=3, 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: 4. Let r(f) = ° 13 i - 6fj + Pk. (a) Find the unit tangent vector T(t) and T(3). | (b) Find the…

A:

Q: x+3 x-3 2x + 5. A student simplified the expression 4 6 and gets the answer 12. What did the student…

A: For addition two fractions with different denominators, we have to make denominators same using…

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: 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: 1. Obtain the directional derivative of: a.. f(x,y) = x²-4x³y² at the point (1,-2) in the direction…

A: Step 1:

Q: Find the differential equation whose general solution is y = cvh x + cv2 e^x %3D

A:

Q: A supplier for St. LeRoy Hospital has introduced quantity discounts to encourage larger order…

A: Given that, Ordering cost (S) = 45 Demand (D) = 936 Holding Cost = 25% pf Price Now  we will find…

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

A: The objective is to find the directional derivative of the given function h(r,s,t) along the point…

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: 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: 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: