Find and sketch F(x, y). X,Y

Q: Show that the function f defined by (r, y) = (0,0) f(x, y) = { 22 + y (r, y) # (0,0) x + y

A:

Q: Use e – 6 definition and show that the function 4x² – y? if (r, y) # (1, –2) 2r + y f (r, y) = • 4,…

A:

Q: Let f(x, y) be the function Vlxy|. Which one of the following statements is correct?

A:

Q: The set of all points where the function f(x) = x |x| is differentiable is (A) (-∞, ∞) (B) (-∞, 0) U…

A:

Q: Let f(x, y) = x* /I Evaluate f(3, 0)

A:

Q: Determine the global extreme values of the function without using calculus. f(x, y) = x + y, 0 < x <…

A: Given Data: Function: fx, y=x+y Range of x: 0≤x≤2 Range of y: 0≤y≤2   The maximum value of x and y…

Q: Find fry for f(x, y) = In(x – y).

A:

Q: : Express the function f (x) = e") to the form u(x,y) + iv(x,y).

A:

Q: Prove that y = x- 2 is differentiable and calculate y'.

A: Given: The function, y = x-2

Q: Evaluate F dr, where C goes along the curve {x* + y* = 1, z = 2} from (1,0, 2) to (b) (0, 1, 2).

A:

Q: Find f(-1,1,0) f(x,y,z)=(2xy-y^2+z)/(x^2+3xy+z)

A:

Q: 11. Verify that the conclusion of Clairaut's Theorem holds for the function: f(x, y) = e*Y sin(y)

A: The given function is: fx,y=exy siny To verify that the conclusion of Clairaut's theorem hold for…

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

A:

Q: Let y = f(x) be a derivable function implicitly defined by the equation x2 + y2 = 1 . Calculate y'.

A: The power rule of differentiation to differentiate a function of the form y=xn,is stated as…

Q: Write the function z = xy + x - y in the form F(x, y, z) = 0.

A: Given: z=xy+x-y for writing given function in the form of Fx,y,z=0 we need to do transportation of z…

Q: Assume that f(r, y) is a function given by if (r, y) # (0,0), f(r, y) = 0 if (r, y) = (0, 0).

A:

Q: Show that if f (x, y, z) = 0 then = -1.

A:

Q: Given the function: f(x,y, z) = x°y2² + æy° +y°z Find а. fazy: (x, y, z) b. fazyz(1, –1, 1) -

A: Given the function :  f(x,y,z) = x3y5z7 + xy2 + y3z

Q: 4. Let f(x, y)=2x*y' . Find f,(x,y)

A:

Q: Find all values of x and y such that fx(x, y) = 0 and fy(x, y) = 0 simultaneously f(x, y) = 1/x +…

A: Given:fx,y=1x+1y+xyfxx,y=0fyx,y=0

Q: Let f(x, y) = xy - 4x on

A:

Q: Find ( fx fy, fzf xy f yx fxyz f zzx) for the function: f(x, y, z) = xyz + x²y + z³x + x²y?

A: To find the differentiation of the function

Q: Show that the function y = x¹/², x > 0, is strictly concave

A: Given that y=x1/2 Differentiate both sides w.r.t x, y'=12x1/2-1y'=x-1/22 Again differentiate w.r.t.…

Q: If a function y = f(x) satisfies = y, %3D then %3D dr y = e".

A:

Q: find fsubxz if f (x, y, z) = ye^x + x ln z

A:

Q: f(x,y) = x+ xy

A: Find and sketch the domain of f(x,y0=x+xy

Q: If f(x) = 2sin-'(u) where u =L, then: f'(x) = %3D f (2) =

A:

Q: Let f'(x) = f(x) = V cos(eztsin(2=)) 4.

A:

Q: Find fy (x,y) if f(x.y) = (x° +y®)* fxy (X.y) = %3D

A: Topic = Derivative

Q: Find fy (X,y) if f(x,y) = (x° + y°)°. ху Exy(x.y) =

A: Topic: differentiation

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

A:

Q: Let f(x, y) = (- (3x + y))'. Then %3D drðy af

A:

Q: Let f(x, y) = y cos (xy), then f.(x, y) = fy(x, y).

A:

Q: Find fxx, fxy, fyx, and fyy if f(x, y) = sin²(x – 3y) %3D

A: f(x,y) = sin2(x - 3y) fx = 2sin(x - 3y)cos(x - 3y) fy = 2.(-3).sin(x - 3y)cos(x - 3y) = -6sin(x -…

Q: Find the linear approximation of the function f(x)= cuberoot(1+x) centered at 0. Use this to…

A: For the solution follow the next step.

Q: The values of fx , f y and f, at (1,1,1) for the function f (x,y,z) = x² + xyz +z are fy= Choose. +…

A:

Q: Find the inflection point of the function f(x) = x°In(x). %3D (x, y) = (

A: The given function is fx=x5lnx

Q: Consider z as function of the variables x and y, it is defined by :

A:

Q: дхдуда dydzdx dzdxdy

A:

Q: The set of all points where the function f(x) = i-e¨ is differentiable is (A) (0 , ∞) (B) ( –0, ∞)…

A: We find the set of all points where the given function f(x) is differentiable.

Q: f: (Z, +) → (Z, +) where f(x) = 2x. f: (R, +) → (R*, .) where f(x) = 2*

A: We will use definition of isomorphism

Q: Q1// Find and sketch the Domain of f(x,y) In (x' y)

A:

Q: Find the function f(x,y,z) with a magnitude y.

A: A vector is a quantity that has both magnitude and direction. It can be also defined as the…

Q: Let f: R" x R → R define as follows f(x, y) = then f is

A: Given that: f:Rn×Rn→R define as follows fx,y=∑xiyi¯i=1n. The objective is to determine the value of…

Q: 2. If f(x, y) is a function of y only, then S" S fdxdy Si fdy. %3D

A: Given query is to find statement is true or false.

Q: If z = y + f(x^2-y^2), where f is differentiable, show that y(∂z/∂x) + x (∂z/∂y) = x.

A:

Q: Prove that (x – 2)dx = – f,(x – 2)dx |

A: To prove that:∫13x-2dx=-∫31x-2dx

Q: Determine if F(x, y) = (x – y)i + (x – 2)j is conservative.

A: The conservative nature of the vector field depends upon the curl of the given vector field.