3. At point (1,0,3) on the surface f(x,y) = 2x^2 + 3 y^2+ z^2-11, the directional derivative in the direction v = i + 2j +k is *

Q: Please show your answers to at least 4 decimal places. Suppose that f(x, y) = ry. The directional…

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Q: f(x, y) = ln (2x) In (3y) + x - y - xy - 3, then fyz (2,-) is equal to

A: Given :fx,y=ln2xln3y+x-y-xy-3

Q: What is the gradient vector of a differentiable function ƒ(x, y)? How is it related to the…

A: The objective is to write what is the gradient vector of a differentiable function ƒ(x, y) and how…

Q: 4. Find equations of the tangent plane and the normal line to the surface yz = arctan(2x+z) at the…

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Q: Write down the the definition (in terms of limits) of the directional derivative and use it to…

A: We have to write down the definition of the directional derivative and also find the directional…

Q: Find a point on the surface x+4y--z² =1 where the tangent plane is parallel to the plane x+4y- z =…

A: we need to find gradient of given surface to know about direction of normal vector to tangent plane

Q: Integrate f(x, y, z) = x2 +y – z over the line segments from (0, 0, 0) to (1, 1, 0) and then to the…

A: According to the given information, it is required to integrate the function over the line segment.…

Q: 25 at the point ( 1, -1, 2 ).

A: Given that : The surface  8x2+y2+4z2 = 25 , point = ( 1, -1, 2 ).

Q: 6. Where does the tangent line to r = at the point (1, 0, 1) intersect the y-z plane.

A: Given:

Q: Find all equations of the tangent line to the common curve of the two surfaces with equations z = x²…

A: follow next step

Q: The maximum directional derivative of f(z,y,2) sin(zy)-ya +10 at (-1, 2, 0) is Question 5

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Q: Explain how a directional derivative is formed from the two partial derivatives ƒx and ƒy.

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Q: 8. Find the directional derivative off at the p in the direction of v = () of f(x, y, z)=x²exx, p =…

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Q: wn is bounded by the line y = − 5x + 4, - -axis and the y-axis. y X

A: we will find the area.

Q: Integrate ƒ(x, y, z) = x - 3y2 + z over the line segment C joining the origin to the point (1, 1, 1)

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Q: The value of the line integral fydx + xydy over the straight-line path C from (0, 0) to (1, 2)…

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Q: 5) Find the equation of the tangent plane to the surface exyz= x + 2y + 3z at the point (3,-1,0).

A: Find tangent plane to the surface

Q: 2.Evaluate the total derivative of u with respect to x for u = 4x4+3y² + 3z² when y = sinx and z =…

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Q: The gradient vector of the function f(x, y) = cos(4x - 6y) is (4 sin(4x - 6y), -6 sin(4x - 6y)).…

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Q: Choose the gradient of the function f defined by f(x, y, z)= In[1 + (17xy + xz +9yz)²].…

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Q: independent

A: We will solve the problem.

Q: 32 Suppose that f(x, y) = x°y². The directional derivative of f(x, y) in the directional (1, 2) and…

A: Given problem:- Suppose that f(x, y) = x3 y2 . The directional derivative of f(x, y) in the…

Q: Compute x²z ds where Cis the line segment from (0,6,–1) to (4,1,5).

A:

Q: The equation of the tangent plane at the point P(1, 1,-1) on the surface z = f(x, y) = 4 - -* is x +…

A: As per bartleby guidelines we are supposed to answer only one question per post. This post contains…

Q: Find a set of symmetric equations for the normal line to the surface xyz = 12 at the point (2, −2,…

A: The normal line to the surface xyz = 12 at the point (2, −2, −3).

Q: Give 1 problem of partial differentiation of function of U with respect to 3 independent variables…

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Q: Suppose that f(r, y) the point (r, y) 3 (6, ry. The directional.derivative of f(z, y) in the…

A: Given:  fx, y=xy To Find:  To find the direction derivative of fx, y at the point x, y=6, -4, in the…

Q: Evaluate the line integral Sc (2x² − 3y) dx + xy dy, where the curve/path C is the line 3 y = 2/2 x…

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Q: Use implicit differentiation on the equation 2e9Z – 10xz +x cos(y) = 5 to find - and ôx -2xzewz +x…

A: This is partial derivative so while differentiate with respect to one variable consider other…

Q: Integrate f(x, y, z) = x2 +y – z over the line segments from (0, 0, 0) to (1, 0, 1)  and then to the…

A: According to the given information, it is required to integrate the function over the line segment.…

Q: Find both first partial derivative Z = 15x x/y az az ду

A: As we know that: The the Power law: ddxxn=nxn-1 From the given problem: z=15xy

Q: The directional derivative of f(x, y) = ln(xy) + x² at the point (-1, 1) in the direction of from…

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Q: Suppose that f(x, y) = x°y. The directional derivative of f(x, y) in the directional (– 2, – 1) and…

A: Explained below

Q: How do I find the bounds in which I integrate a curve that is rotated about an axis?

A: To find the bounds, it is necessary to check whether we have to find the surface area or volume. In…

Q: If f(x,y) = ln(xy) + x^2y^2, how do I calculate the second directional derivative of f in the…

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Q: In what directjon from the point ( 1, 3, 2 ) is the directional derivative of 6 = 2 xz-y a maximum ?…

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Q: Show that the function has partial derivative at the point (0,0) but is discontinuous at this point.

A: solve the following

Q: B) Find the derivative of the foiiowing: 1) y = 2sin2(5x) ,2) y = x, 3) xsin-14y = y tan-14x 4) y =…

A: As per the company  guidelines we have to solv first 3 subparts if suborats are not mentioned  So…

Q: What is the gradient of f(x, y, z) = x³z2 + y³z +125z - 1 at P(5,5,-1) ?

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Q: We have to find parametric equation for a line that is tangent (intersection) of the two fields…

A: We have to find parametric equation for a line that is tangent (intersection) of the two fields…

Q: Calculate the curve integral ∫c ( 3x2 - 3yz + 2xz )dx + ( 3y2 - 3xz +z2 )dy + ( 3z2 - 3xy + x2 +2yz…

A: Using green's theorem to find the line integral.

Q: 3. Evaluate the gradient of S(1, y, 2) = In(cosh z+ y) - arctan| at (1,y) = (7/2, 1).

A: Given that fx,y,z=lncosh x+y-z2 arctanx2y2+z2 To find the gradient of f(x,y,z) :…

Q: Show that the surfaces S1 : 4x + y° + 9z² = 108 and S2 : xyz = 36 are tangent at the point (3, 6,…

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Q: A bee was flying upward along the curve that is the intersection of z = x⁴+xy³+12 with the plane…

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Q: What is the rate of increase of the scalar function f(x,y,z) = sin (πx/3) sin (πy/2) e^-2z from the…

A: See the attachment

Q: Compute the equation of the tangent plane to the surface: y = 1 - x2 - 2z2 At the point (0, 1, 0)

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Q: (b) Show that the function defined by xy √√√²+y² f(x, y) 0 if (x, y) = (0,0) is not differentiable…

A: We have to show that the function defined by…

Q: Find the work done by the gradient of ƒ(x, y) = (x + y)2 counterclockwise around the circle x2 + y2…

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