Where is the function f(r, y) = x/y continuous?

Q: What does it mean for a function of two variables, f (x, y),to be differentiable at a point (a, b)?

A: A function differentiable at a point has a derivative that is defined at that point. This is defined…

Q: dy If F(x.y) = 0 and y is a differentiable function of x, explain how to find dx

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Q: Please find the gradient of f(x, y) = ln(x² + xy²) at (2, 1)

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Q: consider the function f(x, y) = esin(x), Find the maximum rate of change of f at the point (, 1).

A: The direction of maximum increase of f is given by ∇fx,y.Maximum value of Du→fx,y or rate of…

Q: Illustrate local linearity for the function f (x) = xsinx at x = l.

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Q: Fundamental Theorem of Calculus.

A: ∫abfx dx

Q: Use the linear approximation of f(x) = at r = 0 to approximate f(-0.1). 1+r

A: Use the linear approximation of f(x)=1/(1+x) at x=0 to approximate f(-0.1).

Q: How is the linearization of f (x, y) at (a, b) defined?

A: given,          any function fx,y at a,b

Q: Calculate fxxyz for f (x, y, z) = y sin(x + z).

A: We first differentiate the given function with respect to x twice. Then y and z will be treated as…

Q: Calculate fxxyz for f(x, y, z) = y sin(x + z).

A: For a function in several variables, partial derivative with respect to one variable say x can be…

Q: How is the linearization of f(x, y) centered at (a, b) defined?

A: To define linearization of a function f(x,y) at point (a,b).

Q: Let { sin(r-y) |r|+ |y| 0 (x, y) = (0,0) f(x, y) = Is f continues at the origin? Why?

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Q: Find the maximum rate of change of f (x, y) = xln /x2 + y2 at (1,2) and direction in which it…

A: To find the maximum rate of change of fx,y=xlnx2+y2 at 1,2 and direction in which it occurs.  First,…

Q: What is the linearization L(x, y) of a function f (x, y) at a point (a, b)? How is L(x, y) connected…

A: Linearization L(x,y) of a function f(x,y) is given by the formula

Q: Groph of f(x)= (x² Is there a Is f differentiable at X=o? Justify %3D sharp Corner at X=O ?

A: Consider the given graph. fx=x2+0.0001 Now, draw the graph.

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: 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 partial derivative of function respect to y* f(x, y) = x² + y/y? %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…

A: Consider the function: fx,y,z=xlnyz Differentiating with respect to “x” then,…

Q: Show that the function defined by xy √x²+y² f(x, y) {{ = 0 if (x, y) = (0,0) is not differentiable…

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Q: d dx y' z' y" z"

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Q: The gradient of f(x, y) = xy at (x, y) = (2, 3) is

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Q: Find fr and fy- f(x, y) = 7e dt f-(x, y) = f,(x, y) =

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Q: Find the derivative of the function at Po in the direction of A. f(x,y,z)=3 ex cos (yz), Po(0,0,0),…

A: Solution: f(x,y,z) =3exCos(yz) P0=(0,0,0)

Q: ( 2x2 , xs1 Dose f(x) = continuous at x =1?why? %3D &+ 1 , x >1

A: Explanation of the solution is given below....

Q: Find a linear approximation of the function f(x) = V1-x at a = 0. %3D

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Q: Find the gradient of the functions below a)f(x, y) = In Vx? + y?

A: Here we will find out the required value.

Q: Find the derivative of the function at Po in the direction of A. f(x, y, z) = x2 + 2y2 – 3z?, Po(1,…

A: We can solve this as follows:

Q: Find fyxy. f (x, y) = x"y® – 20°y +x f yay YxY

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Q: Verify that the conclusion of Clairaut's Theorem holds for the function: f (x, y) = e*y sin(y)

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Q: Find He valve of fe2) when fg functions such that are dilferentrable %3D g(x) >o 1 for all x, while…

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Q: Find the gradient of the functions below. a)f (x, y, z) = sin(xyz)

A: Here we will find out the required value.

Q: Let f(x, y) = xe". What is the maximum rate of change of f at the point (2,0)?

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Q: The gradient of f(x, y) = xy at (x, y) = (3, 1) is

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Q: Let z be a function of x and y, while x and y are functions of t. Explain how to find dz/dt.

A: Let z be a function of x and y, while x and y are functions of t. Then, dzdt=∂z∂x·dxdt+∂z∂y·dydt

Q: Show that w=f(z) =3ix+y dose not satisfy C.R.E. thus it is not analytic function

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Q: Find the linear approximation of the function y = x' at point xo 1 О а. у %3D Зх — 2 -

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Q: Let f(r, y) 3ry? when (x, y) + (0,0) and f(0,0) = 0. g²+2y! At which points is f continuous?

A: The given function is: This function is continuous at a point if at that point limit exists and the…

Q: Find the derivative of the function at Po in the direction of A. f(x,y,z) = 3 ex cos (yz),…

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Q: What is the derivative of y = x + Vx + 1 ? y' = 2(x + 1) + 1 O y' = (x + 1) + 1 %3D O y' = (x +1)+ 1…

A: Let's Solve, Answer: Option C

Q: The gradient of f(x, y) = xy at (x, y) = (3, 3) is

A: Given problem:- Find the gradient of f(x, y) =xy at (x, y) =(3, -3)

Q: Let f(x, y) = (x² +(G))°. Determine the directional derivative of f at the point (1 0) in the…

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Q: Suppose F(x, y) = 0 and y is a differentiable function of x. Explain how to find dy/dx.

A: It is given that F(x, y) = 0 and y is a differentiable function of x . For the function F(x, y) = 0…

Q: Find f and fy- f (x, y) = 9e dt f (x, y) = %3D fy(x, y) =

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Q: What is the maximum value of the directional derivative of f(x, t) = f (x, t) = x² + t²/8 – 10 at…

A: Note: The directional derivative of a function is the rate at which the function changes at a…

Q: find the degree of Precition @F(x)= X

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Q: If f'(x) = x*, what is f(x)? (Use C for the constant of integration.) %3D f(x) = %3D

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