Using a Function (a) find the gradient of the function at P, (b) find a unit normal vector to the level curve f (x, y) = c at P, (c) find the tangent line to the level curve f (x, y) = c at P, and (d) sketch the level curve, the unit normal vector, and the tangent line in the xy-plane.                                                         f(x, y) = 9x2 + 4y2,                                                                                                  c = 40,    P(2, −1)

Q: Let f (x, y, z) be a function such that : (i) the function f (x, y, z) decreases most rapidly at the…

A:

Q: Fourier's Law of heat transfer​ (or heat​ conduction) states that the heat flow vector F at a point…

A: Given that,

Q: Tutorial Exercise Use the gradient to find the directional derivative of the function at P in the…

A: Please refer the attached image for complete solution.

Q: Using a Tangent Line Approximation In Exercises 1-6, find the tangent line approximation T to the…

A: Since, you have asked so many parts in single request. I will answer first two parts. If you still…

Q: x? y? Level curves Consider the paraboloid f(x, y) = 16 - 16 and the point P on the given level…

A: The equation of paraboloid is We have given That implies,

Q: (x, y) frx (x, y) fyy (x,y) f, (x,y) Point 1 1 Point 2 Point 3 -1 -1 -1 -1 1 Point 4 -1 -1 Point 5…

A:

Q: 3. Find the directional derivative of the given function f at the given point P in the direction of…

A: 3. From the given problem:   fx,y,z=x2+y2+z2 ; p1,2,2 ; a=3,2,1   As we know that the expression for…

Q: Fluid runs through a drainage pipe with a 10-cm radius and a length of 30m (3000 cm). The velocity…

A: We are given the following table. x 0 1 2 3 4 5 6 7 8 9…

Q: Find the gradient of f . (b) Evaluate the gradient at the point P. (c) Find the rate of change of f…

A:

Q: x? y? Level curves Consider the paraboloid f(x, y) = 16 - 16 and the point P on the given level…

A:

Q: 3. For f(x,y,z)= In(x² + y– z), a.) find the gradient of f b.) evaluate the gradient at (1, 1, 0)…

A: ∇f = ∂f∂x,∂f∂y,∂f∂z Directional derivative (d) = u→.∇f

Q: Using the Hough transform i) Develop a general procedure for obtaining the normal representation of…

A: (i) to Develop a general procedure for obtaining the normal representation of a line from…

Q: Computing directional derivatives with the gradient Compute the directional derivative of the…

A: Given: f(x,y)=3x2+y3, P(3,2) ; 513,1213 To determine: Directional derivative of the given function…

Q: f (x, y) = x ln (), P(3, 1), u = -i+ i Р(3, 1), и

A:

Q: Nonuniform straight-line motion Consider the motion of an object given by the position function…

A: (a) Consider t1 and t0 as two values of t. Obtain the difference between r(t1) and r(t0).…

Q: Find the equation of the tangent plane to z=e^y+x+x^3+5 at the point (5,0,136)

A:

Q: Consider the function f(x.y,z) = 3x +y +z? + 3, the point P(2,0,4), and the unit vector u = a.…

A: Use gradient formula and magnitude to solve this

Q: gradient field that corresponds to function (x, y, z) = y2 -x2 +x e=2 - y3 z

A: This is the question from Vector Calculus.

Q: a. Find the gradient of f. b. Evaluate the gradient at the point P. c. Find the rate of change of f…

A: The given function is, f(x,y,z)=y2exyz. a. Obtain the gradient of f as shown below.…

Q: derivative Q3: For the surface f(x, y, z)= In (xyz), find: (1) the gradient of f at (1,1,2), (2) the…

A: As per our guideline, we are supposed to solve only first three subpart. Kindly repost other subpart…

Q: A normal line to a surface S at a point (x, y, z) E S is a line perpendicular to the tangent plane…

A:

Q: Proof of Stokes’ Theorem Confirm the following step in theproof of Stokes’ Theorem. If z = s(x, y)…

A:

Q: Point Func tion h(x.y)-7ycos (x-y) Co,Ti/3) Dn(o,1/3) = %3D

A:

Q: A normal line to a surface S at a point (x, y, z) E S is a line perpendicular to the tangent plane…

A:

Q: the gradient to find the directional derivatve of the function direction of Q. 8. f(x,y) = e' sin x…

A:

Q: Exercise. Find the equations of the tangent and the normal at the point indicated. 1. y = 3x2 -2x +…

A: As per company guidelines we can solve first question. I hope that the given solution will help you.…

Q: y Consider the surface of equation z = What is the equation for the tangent line to S at x2+y4 * the…

A: Solution

Q: f(x,y)=3 e^x cos y, (a,b)=(0,π/4), and v⃗ =(2,3).  Calculate the directional derivative of f at the…

A:

Q: Using Properties of the Derivative In Exercise 26, use the properties of the derivative to find the…

A:

Q: 3. Let f(x, y) = ey and a point P(1,0) a. Solve for the gradient of f at the point P. b. Find the…

A: Given: The function, fx,y=exy and the point, P1,0. (a.) To solve: The gradient of f at the point P.…

Q: 47-50. Level curves Consider the paraboloid f(x, y) = 16 %3D - - 4 16 and the point P on the given…

A:

Q: Using Properties of the Gradient In Exercises 61-66, find the gradient of the function and the…

A:

Q: (a) Show that a differentiable function f decreases most rapidly at x in the direction opposite the…

A:

Q: Orthogonal Trajectory of the Curve x2+y2 = 2 In Cx

A: From the given curve; x2+y2=2lncx Now differentiate with respect to x. So,…

Q: Gradient 3. Find the gradient of the following scalar functions. (c) f(x,y)=at (-1.1) (d) $(x,y,z)=-…

A:

Q: (a) Find the gradient of f. (b) Evaluate the gradient at the point P. (c) Find the rate of change of…

A:

Q: a) Find the gradient of f . (b) Evaluate the gradient at the point P. (c) Find the rate of change of…

A: Given that: f(x, y, z)=xy+yz2+xz3

Q: A surface S is described by the equation f(x, y, z) = n where f(x, y, z) = yz + nx²y+ yz³ 3 (a) Find…

A: Given f(x, y, z) = yz + nx2y + yz3 ∇fP⋅P=0 Now,…

Q: (I) Determine the gradient of f. (II) Calculate the gradient at point P. (III) Determine a rate of…

A: Formula: Grad f= (∂f/∂x)I +(∂f/∂y)j +(∂f/∂k)I

Q: Interpret the magnitude of the gradient vector at a point. Choose the correct answer below. O A. The…

A:

Q: Find the WORK done to empty a tank with a (equilateral) triangular base 12 ft on a side and 20 ft…

A:

Q: (1 point) If the gradient of ff is ∇f=2z(i) +x (j) +yx (k) and the point P=(−8,−8,−2) lies on the…

A: Let r=xi+yj+zk be the position vector of any point P on the surface.The position vector of the given…

Q: f(x, у) — х/у, Р(2, 1), и %3D i +j

A: "Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Integral Calculus: A particle moves according to the given velocity function over the given…

A:

Q: Slopes, Tangents, and Normals In Exercises 31–40, verify that the given point is on the curve and…

A:

Q: Evaluate. The differential is exact. HINT: APPLY: Fundamental theorem of line integral. The initial…

A: To Evaluate: ∫0, 0, 06, 9, 85x+1e5x dx+z dy +y dz Given that the differential is exact and the…

Q: f(x,y,z)=5sin(xyz), (a,b,c)=(1,1,π/4), and v⃗ =(5,−2–√,5).  Calculate the directional derivative of…

A: as per guidelines, I can answer only three subparts of a question.

Q: (d) d dt [r(t) ∙ u(t)]             (e) d dt [r(t) × u(t)] (f) d dt [u(2t)]  26. r(t) = sin ti +…

A:

Q: Suppose f(x,y)=x/y, P=(−2,−3) and v=4i−3j A. Find the gradient of f. B. Find the gradient of f at…

A: