01. The equation of the tangent plane to the surface f(x, y) at the point (1,1) is 2x + 2y = 9, find: 1. The gradient of the surface at point (1,1): 2. The derivative at point (1,1) in the direction of v = i+2j: 3. The direction(s) at which the surface has a directional derivative of 2 at point (1,1);

Q: |a) Compute the equation of the tangent plane to the level surface g(z, y, 2) = r²y +2y°z – 3z*x = 3…

A: Hello. Since your question has multiple parts, we will solve the first  parts for you. If you want…

Q: If the gradient of f is ∇f=y3j−xi+zyk and the point P=(−8,6,2) lies on the level surface f(x,y,z)=0,…

A: To find the equation

Q: 1. The temperature at the point (r, y) on an unevenly heated plate is given by T = f(r, y) = 100+…

A: Given f=100+5x2+15x+10y2gradient of f∇f=∂f∂xi+∂f∂yj     =10x+15i+20yjAt (2, 1)∇f=10x+15i+20yj…

Q: Obtain the gradient to a curve with parametnic equations given by and y= X= In 2 2t when t-1

A:

Q: 03. The equation of the tangent plane to the surface f(x, y) at the point (1,1) is 2x + 2y = 9,…

A: the surface is fx,y the gradient to the surface at (1,1) is ∇fx,y Let the value of the gradient is…

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: Consider the function z = f(x, y) = x° + x² cos y What is the directional derivative at (1,0)) if…

A:

Q: Find the directions in which the directional derivative of f (x, y) = ye*y at the point (0,2) has…

A:

Q: 3. Given that $(r, y, 2) = 1 + – y² +: Find the followings at (1, –1, 1): (a) The directional…

A:

Q: Determine the gradient of f(x, y) *sin(4y) at (x, y) = ( – 2, 3). Round to 2 decimal places. V f( –…

A:

Q: Find the directional derivative of the function at P in the direction of v. f(x, y, z) = xy + yz +…

A:

Q: b) Find the directional derivative of f (x, y) = xy + e*°vy + 1 at (-1,1) in the direction of the…

A: f=xy+ex3y+1 take the partial derivative with respect to x   fx=∂∂ xxy+ex3y+1 fx=∂ ∂ xxy+∂ ∂ xex3y+∂…

Q: Find the gradient of the function f(x,y) = /4x+2y at the point (- 1,4). Then sketch the gradient…

A:

Q: Use the gradient to find the directional derivative of the function at P in the direction of v. h(x,…

A:

Q: Find the directional derivative of f(x, y, z) = x²y + y²z v = at P(1,2,3) in the direction of %3|

A: In geometry and physics and its engineering applications, we use two kinds of quantities, scalars,…

Q: 1. Determine if the gradient of the following velocity function is irrotational: V (x, y, z) = 3x³y²…

A:

Q: For f(x,y, z) = x² – (1 – y)² + z?. Find directional derivative of f at P(1,1,1) in the direction of…

A: The directional derivative of a function f  in the direction of the vector u is given by…

Q: Suppose we know that for a function f we have Vf(x, y) = (6x, 6). Find the directional derivative of…

A:

Q: If the gradient of f is Vƒ = 3x i + z² j+ 2yz k and the point P = (4, –6, –9) lies on the level…

A:

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

A: Given

Q: Q1. The equation of the tangent plane to the surface f(x, y) at the point (1,1) is 2x + 2y = 9,…

A:

Q: If the gradient of f is Vf = r'j- 3yi+ 2zz k and the point P = (-4,-4, 1) lies on the level surface…

A:

Q: Find the directional derivative of f(x, y, 2) = xz+ y?, at (1, 2, 3) in the direction of i = i+j+ k.…

A:

Q: Let f(x,y)=x3- x - 3x2y + y3 (a) At the point (x, y) = (1, 2), in what direction does f increase…

A: Since you have posted a question with multiple sub-parts, we will solve the first three subparts for…

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

A: Given that: f(x,y)=x2y at the point (1,1) Ellipse: x2+2y2=1 at the point (1,0)

Q: Find the gradient for the function f(x, y) = x5 sin(xy) at the point (, 10) Find exact values. No…

A: To find the gradient of a function (which is a vector), differentiate the function with respect to…

Q: If the gradient of f is ∇f=yj⃗ −xi⃗ −4zyk⃗  and the point P=(−7,−8,−3) lies on the level surface…

A: an equation for the tangent plane to the surface at the point P

Q: Given f(x,y,z) = x2 + y2 + z2, find the maximum value of the directional derivative (df/ds) at the…

A: Consider the provided question,

Q: If f (x, y) = x² + 4y² , use the gradient vector Vf(3, 1) to find the tangent line to the level…

A:

Q: Let F(x, y) = [2ry² +x, 2r²y + y]. Find all functions f with gradient F. Find the derivative of f in…

A: # we are entitled to solve 3 subparts at a time ,please resubmit the other subparts if you wish to…

Q: If f(x, y) = xy, find the gradient vector Vf(7, 5) and use it to find the tangent line to the level…

A:

Q: Compute the directional derivative of f (x,y)= at the point (1,1) in a direction normal to the…

A: The directinal derivative is given below

Q: 1. Let f(x, y) = x cos(2x+ y). a) Find the value of the directional derivative of f(x, y) at in the…

A:

Q: Find the directional derivative of f(x, y) = sin(x + 2y) at the point (1, -4) in the direction 0 =…

A:

Q: If f(xr, y) = x² + 2y², use the gradient vector Vf(5, 3) to find the tangent line to the level curve…

A:

Q: B-For the surface z² = x² + y² find the directional derivative at the point (√2, √2,-2) in the…

A:

Q: 2y 6. Given f(x, y) = y a) find the directional derivative of f (x,y) at (1,-2) in the direction of…

A:

Q: Find the gradient Vf for the function f(x,y)= e* sin(zy) and the directional derivative at the point…

A: to find the gradient take the partial derivatives of the function then substitute the x and y values…

Q: Q2: a) If W = F(x ,y), where x =v²-g and y = 2vg calculate W +W, b) What is the directional…

A:

Q: If the gradient of f is Vf = x³ } – zỉ+ 2yx k and the point P = ( surface f (x, y, z) = 0, find an…

A:

Q: If f(x, y) = x²y and ʊ = 47 – 37, find the directional dervative at the point P = (3, 6) in the…

A:

Q: 2. For the function f(x,y) = 3x + 4y – xy a) Vf(1,2) = b) Find the directional derivative of f at…

A:

Q: For f(x,y,z) = x² – (1 – y)² + z?. Find directional derivative of f at P(1,1,1) in the direction of…

A: Since there are two questions posted, we will answer the first question posted (1). If you want the…

Q: Find the gradient of the function at the given point. z = x?y, (7, 1) Vz(7, 1) = Find the maximum…

A:

Q: Find the directional derivative of f(r, y, z) = e cos(ryz) at (0,1,) in 2 - 1 I- 2 the directions…

A: We have to find the directional derivative of f(x,y,z) at 0,1,12 in the directions parallel to the…

Q: Find the values of constants a,b.c such that the maximum value of the directional derivative of f…

A:

Q: For the given surface f (x, y) = 2 + sin(xy) at the point (1, 0, 2), find the following: a) Gradient…

A:

Q: 1. Determine the directional derivative of the surface f(x, y) = 3x? + y³ at the point P(1,2) in the…

A:

Q: Use the gradient to find the directional derivative of the function at P in the direction of PQ g(x,…

A: Given that: g(x, y, z)=xye10z,     P(4, 12, 0), Q(0,0,0)

Q: Use the gradient to find the directional derivative of the function at P in the direction of PQ.…

A: Given that, the function is gx,y,z=xye8z and the points are P3,12,0 and Q0,0,0.…