The temperature at the point (x, y) on a metal plate is T = x² + y2 Find the direction of greatest increase in heat from the point (1, 4).

Q: Find the maximum rate of change of f(x, y) = In(x² + y?) at the point (-5, -5) and the direction in…

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Q: The temperature in degrees Celsius on the surface of a metal plate is given by T(x, y), where x and…

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Q: Find the direction derivative of f(x, y, z) = x²y -zx -yx at the point (1,-1,1) in the direction…

A: Directional derivative using gradient

Q: Find the maximum rate of change of f at the given point and the direction in which it occurs. Rx, Y,…

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Q: Find the direction in which the maximum rate of change occurs for the function f(x, y): 4x sin(xy)…

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Q: F(X, y,z) = 2x -y? +z?

A: F(x,y,z)= 2x-y^2-z^2 at point (4,-4,2) df/dx= 2 df/dy=-2y df/dz= -2z

Q: Find the maximum rate of change of f at the given point and the direction in which it occurs. f(x,…

A: The maximum value of a function f occurs in the direction of the gradient of the function f and this…

Q: 4. y = x2--Inx x = 1 ve x = e

A: Topic- application of derivatives to find angle between curves

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

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Q: Find the direction in which the maximum rate of change occurs for the function f(x, y) = 3x sin(zy)…

A: The maximum rate of change of a function f(x, y) at (a, b) occurs in the direction ∇f(a, b)  where…

Q: Find the direction in which the maximum rate of change occurs for the function f(x, y) = 5x sin(xy)…

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Q: Find the directions in which the directional derivative of f(x,y) = x^2 + xy^3 at the point (2,1)…

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Q: Find the maximum rate of change of f at the given point and the direction in which it occurs. f(x,…

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Q: Find the equation for the tangent plane and the normal line at the point Po(1,1,3) on the surface…

A: Given problem:- Find the equation for the tangent plane and the normal line at the point Po(1,1,3)…

Q: Find the directional derivative of f(x, y) = x2y3 + xy2 in the direction ~v =< −3, 7 > at the…

A: f(x, y) = x2y3 + xy2 Please see the white board for the partial derivatives at the point (-1,…

Q: Find the direction for which directional derivative of f (x,y) = 3x² – 4xy + 2y² +29 at (-2,3) is…

A: Formula: The maximum directional derivative of f(x, y) at (a, b) is given by ∇f(a, b) and direction…

Q: Find the direction in which the maximum rate of change occurs for the function f(x, y) = 3x sin(xy)…

A: To find the Direction in which the maximum rate of change occurs for f(x,y)=3xsin(xy) at point (1,3)…

Q: Find the minimum rate of change at (2,-2,0) and it's direction for f(x, y, z)= =. zy² I in the…

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Q: Find the directional derivative of the function f(x,y) = y² Inx at the point (1,2) in the direction…

A: Given function, f(x,y)=y2 ln x Point 1,2 and vector u=3,4 The unit vector of u is…

Q: Which direction is the directional derivative of the function f (x,y, z) = x2 – 2yz at point…

A: Solution: The function is fx,y,z=x2-2yz The point is P1,1,1 We have to find the direction in which…

Q: The temperature at a point (x, y, z) is given by T(x,y,z) = 200 e-x- 3y-9z) where T is measured in…

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Q: Find the maximum rate of change of f at the given point and the direction in which it occurs. f(x,…

A: Gradient problem....

Q: Find the maximum rate of change of f at the given point and the direction in which it occurs. f(x,…

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Q: Find the directional derivative of the function f(, y) = In(x +y°) at the point (- 1,3) in the…

A: As per our guideline we are allowed to do 1 question at a time. Please post other questions next…

Q: • Find the direction in which f(x,y) = yeY increases most rapidly at the point (0, 2). %3D

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Q: Find the direction in which the maximum rate of change occurs for the functio f(r, y) = 2x sin(ry)…

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Q: For f(z, y) is: = 5a sin(xy) at the point (2, 4), the direction in which the maximum rate of change…

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Q: Find the differential of f(x, y) = Vr2 + y³ at the point (2, 3). df = Then use the differential to…

A: given function is f(x,y) =x2+y3 we know, for the function z = f(x,y), the total differential of the…

Q: 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…

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Q: Find the gradient when x = and y = sin (3x). %3D

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Q: Find the maximum rate of change of f at the given point and the direction in which it occurs. f(x,…

A: A vector has 2 components, magnitude and direction which is represented by cos and sin angles. A…

Q: At the point P=(4,1) in the direction v =(i +j )/sqrt2, the directional derivative is approximately

A: Given that the point P4,1 and the direction is v=i+j2 We have to find the directional derivative at…

Q: Find the directional derivative of f(x, y) = Vxy at P(3, 3) in the direction from P to Q(6, -1).…

A: Using partial derivatives at (3,3) in direction of PQ.

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

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Q: Q1) Find equation of line normal to plane 3x + 2y - z = 5 and pass through Origin point.

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Q: Find the directional derivative of the function f(x, y) = 1+5x/ at the point (5, 1) in the direction…

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Q: Find the unit vector u along which the rate of change of the function f(x, y) = x 2 + xy3 at the…

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Q: Find the equation for (a) the tangent plane and (b) the normal line at the point Po(8,0,8) on the…

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Q: Determine the gradient of the curve 3xy + y² = -2 at the point (1, -2)

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Q: Find the direction in which the maximum rate of change occurs for the function f(x, y) 5x sin(xy) at…

A: The given function isfx, y=5x.sin(xy)to find the direction in which the maximum rate of change…

Q: Find the maximum rate of change of f at the given point and the direction in which it occurs. f(x,…

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Q: Find the directional derivative of the function f(x, y) = √√√x + 2y at the point (2, 1) in the…

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Q: Find the directional derivative of the function f(x, y) = In(x + y²) at the point (1, - 1) in the…

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Q: The temperature at the point (x, y) on a metal plate is modeled by T(x,y)=4e^−(x²+y)/2,x≥0,y≥0. (c)…

A: Given: The temperature at the point x,y on a metal plate is modeled by Tx,y=4e-x2+y2, x≥0, y≥0 To…

Q: Find the maximum rate of change of f at the given point and the direction in which it occurs. f(x,…

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Q: Find the directional derivative of the function f(x, y) = ln(x³ + y*) at the point (2, 1) in the…

A: we will find the directional derivative

Q: Find the direction in which the maximum rate of change occurs for the function f(x, y) 5x sin(xy) at…

A: We have to find the direction in which the maximum rate of change occurs for the function…

Q: integrate ƒ over the given curve. ƒ(x, y) = x2 - y, C: x2 + y2 = 4 in the first quadrant from (0, 2)…

A: The given curve C is a circle with center at origin and radius of 2 units. Let the parametric…

Q: Find the directional derivative of the function f(x, y) = In(x + y?) at the point (– 1, – 2) in the…

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Q: Find the direction in which the maximum rate of change occurs for the function f(x, y) = 3x sin(xy)…

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