Find a linear approximation to f(x,y) at (-1, 1). [2хy] y Use your result to find an approximation for f(-0.9,1.05), and compare the approximation with the value of f (-0.9, 1.05) that you get when you use a calculator.

Q: Suppose that the temperature in a given region is given by T(x,y)=200xy(1-x2-2y2). Suppose that you…

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

A: Note: where △f(x,y) = ∂f∂x,∂f∂y

Q: Find the gradient of the function and the maximum value of the directional derivative at the point…

A: The given function is g(x,y)=lnx2+y23 We have to find the gradient of the function and maximum value…

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 f(x, y) 6x at P(3,0) in the x + Y direction of Q(0,–2). NOTE:…

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Q: O Find the directional derivative of f(x, y) = 3x² – 3y² in the direction from P(-,0) to Q(0, 1).

A: Point is given so first find the direction unit vector then  dot product with divergent of f(x,y)…

Q: Find the directional derivative of f(x, y) = 3x2 − 2y2 at (−3/ 4, 0) in the direction from P(−3/4,…

A: The directional derivative is the scalar product of the derivative of the function to the vector…

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: z = Vx4 + yf, fz (1, 2)

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Q: Let f(x,y) be a differentiable function satisfying the equation = xy. %3D ду af and After the change…

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Q: he derivative of f(x,y)=10x^y at (e,1) in the direction of v = is

A: From the expression of the directional derivative:   D.D=∇fpx,y,z·a→a→   Given:…

Q: Find the partial derivative f(x,y) = x7y fx(x,y) = ? fy(x,y) = ?

A: The given function is: f(x,y)=x7y

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

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Q: Use the chain rule to find the derivative of f(z) = 4(4z5+5z“) i

A: Given : fx = 44x5+5x4-12

Q: 5. Find the linear approximation (i.e. the tangent plane) of f(x, y) = Vx/y at the point (9, 4) and…

A: The Local Linear approximation of f at (x,y) using the partial derivative f at (x0,y0) is given by…

Q: The directional derivative of f(x, y) = 2e* cos y at (0, ) in the direction of v = (-6, 8) is

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Q: Find the linearization of the function f(x, y) = /36 – læ² – 2y² at the point (3, -1). L(x, y) = Use…

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Q: 2. Find the equation of the tangent plane to f(x,y) = sin(x² +y) when x = 0, y = T. 3 and r - cost

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

A: Given:        fx,y=4yx   at point 4,5     The rate of change of f is     ∇fx,y=∂f∂x,∂f∂y…

Q: For function f(x, y) = 5- | 2 E find the maximum value of the directional derivative at (3, 2).

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Q: equation of line normal to f(x) = (x +4)1/2 at Q (0,3) is?

A: Given, f(x)=(x+4)12 To find: Equation of line normal to f(x) at Q(0,3)

Q: Find the derivative of the function f(x,y,z) = x² + 2y? – 3z2 at the point v =. Po = (1,1,1) in the…

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

A: The objective is to find the maximum rate of change of f at the given point and the direction in…

Q: 2. Use second order derivative to derive the acceleration, a for an object that falls where its…

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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: According to the given information, it is required to find the maximum rate of change of f at the…

Q: Find the directional derivative of f(x, y) = Vxy at P(9, 1) in the direction from P to Q(12, -3).…

A: Given that: f(x,y)=xy        at P(9,1) in the direction of Q(12,-3)

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: Find the gradient of the function and the maximum value of the directional derivative at the point…

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

A:

Q: Suppose that the temperature in a given region is given by T(x,y)=200xy(1-x2-2y2) . Suppose that you…

A: Given that,Temperature in a given region is given byTx, y=200xy1-x2-2y2You and your friend are at…

Q: The directional derivative of f(x, y) = -e" cos y at (0, ) in the direction of v = (-6,8) is

A:

Q: f (x, y) = 3x^3 −9x+9xy^2. Use the second derivative test to classify the critical point (1,0) as a…

A: Recall: second derivative test : (i)  Firstly find critical points . i.e, fx(x,y) =0 and…

Q: First, compute the gradient of the function f(x,y) = 4+5x²-3y². Then evaluate it at the point…

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Q: Find the gradient of the function and the maximum value of the directional derivative at the point…

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Q: Find the differential of f(x, y) = 3+y² at the point (2, 3). df: ((3x^2)dx+(2y)dy)/(2sqrt(x^3+y^2))…

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Q: Q11) For the z= (2x+3y)10,which is correct ?partial derivative

A: Given,  z = (2x + 3y)10 To find the partial derivatives.

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

A: We have to solve

Q: Find the gradient of the function and the maximum value of the directional derivative at the point…

A: The solution is given as

Q: Find the gradient of the function g(x, y) = 2xey/x , at the given point (2, 0)

A: Consider the given: gx,y=2xeyx,2,0Gradient of the function…

Q: The average rate of change of the function f(z) = 13z +4 on the interval [1, 4] is

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

A:

Q: Find the directions in which f(r, y) = (r+y-2)2+(3x- y- 6)?, increase and decrease most rapidly at…

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Q: Find the gradient of tangent to 3 x2 - x y – y = 23 at the point (3, 1). Enter the exact value of…

A: We have to solve given problem:

Q: Find the maximum rate of change of the function f(x, y) 4y5 at the point (5,4)

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Q: Find the gradient for the curve defined by y + xy = 3 at the point (1,2)

A: Gradient to given curve

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

A:

Q: Find the derivative of the function f (x, y, z) = * ++ at the point (-8, 8,-8) in the direction in…

A: Given thta  f(x,y,z)=x/y+y/z+z/x  To find teh derivative of the function at point p in the direction…

Q: Find the derivative of the function f(x, y) = x²y – 4y3 at the point Po(2, 1) in the direction of v…

A: The given function is:  f(x,y) = x2y - 4y3

Q: The directional derivative of f(r, y) =-e" cos y at (0, 5) in the direction of v = (-6, 8) is

A: Given that fx,y=-excos y at0,π4and v=-6,8

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.