4x + y² R² → R²: f(x, y) = 2xy +1) If there exists a function F(x, y). such that VF(x, y) = f (x, y), find this function F(x, y).

Q: Find ∇f(x, y, z) for the function f(x, y, z) = x2 + y2 − 4z and find the direction of maximum…

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Q: (xy(x²-y²) Let f(x, y) =} (x²+y²) (x, y) ± (0,0)| show that fxy (0,0) + f yx(0,0) (x, y) = (0,0)

A: This question is taken from the partial derivative in which we have to prove the given statement. We…

Q: &r4- V -, determine the Let y=f (x) + C be the antiderivative of F (x) = space) if *=3.6, and y= 17.

A:

Q: The antiderivative of the function f(z): + 9z is +3.0z² +c + 4.5z² + e 6 + 4.5z? + c -6 4.5z2 +c +…

A: Antiderivative of function f(x)=6x2+9x is…

Q: The function f(x, y, z) = x² – y² = z² increases in the direction at the point (1, 1, 1).

A: We need to find if the statement is true or false.

Q: f(z) = (x²+y)+i(y²-x) is analytic

A: Let  fz=fx,yu+iv=x+iy the function must be continuous and differentiable at all points in it's…

Q: e function f(x, y) = (x – 1)² + (y – 1)² subject to the constriant

A: The given function is f(x,y)=x-12+y-12 and subjects to the constraint x2+y2=8 the formula for the…

Q: Find fr, fy, and fz. f (x, Y, z) = z In(x°y²cos(52)) fa = fy = fz = ||

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Q: Let f (x, y) = xy2 + 5. Evaluate df/dy at (x, y) = (2, -1) and interpret your result.

A: Given: f (x, y) = xy2 + 5.

Q: The function f(x, y, z) = x² − y² − z ² increases in the direction 〈六〉 (1, 1, 1). at the point

A: Please check step 2 for solution.

Q: 2. Find a function f(r, y, 2) which makes (yz?, rz?, f(r, y, z)) conservative. Show that your answer…

A:

Q: Find the linearization L(x,y) of the function f(x,y) = x2 - 4xy + 5 at Po(5,4).

A:

Q: Vx? + yZ 49x2 49 [F,(x, y)]² + [f,(x, y)]² 1+ x² + y2 e have [f,(x, y)]² + [f,(x, y)]² = /

A: This is the question from vector calculus.

Q: 2. If F(x, y, z) = 2z3 – 3(x² + y²)z, then verify that Frx + Fyy + F2 = 0. %3D

A:

Q: (a) f :Z → Z, where f(x) = x². g : Z → Z, where g(x) = |æ|². %3D (b) f :Z × Z → Z, where f(x, y) =…

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Q: f(x, y) = In (x²y - x) %3D

A: Here, the given function is: f(x,y)=ln(x2y-x) First to find the first derivatives:…

Q: The local linear approximation of (1- x)2° at x, = 0 is a) 20 - x c) 20 +x b) 1- 20x d) 1+ 20x

A: As per the company guidelines we can solve first question. I hope that the given solution will help…

Q: Maximize the function f(x, y, z) = x² – y², given that x² + 2y² + 3z² = 1. %3D

A: Here, we can use Lagrange multiplier to maximize f(x,y,z)=x2-y2 with constraint x2+2y2+3z2=1. Let…

Q: Consider the function f(x) = 2x³ + 71° – 8z2 – 8. Enter the antiderivative of f(x) + C

A: To find the antiderivative means integration of the given function

Q: I" (D-x) (D +x) (y) =0, then the function y satisfies the DE O y"-x3y=0• O (y'-x) (y'+x) =0• O y"+…

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Q: Use the Chain Rule to find- af when r = 2, t =-1 of the function ar f(x, y, z) = e3xyz cos 2xyz ; x…

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Q: Integrate f(x, y) = y(x² + y³) 3 over the domain x² + y° 0.

A: Given function is fx,y=yx2+y23 and domain is x2+y2≤4 with y≥0 We have to integrate fx,y=yx2+y23 over…

Q: Find V x F for F(x, y, z)= - -xZ + y² i+ -yz x² + y² =j+√x² + y²k.

A:

Q: (xy(x²–y²) f(x, y) = { (x²+y²) (x, y) # (0,0) (x, y) = (0,0) ) show that fxy(0,0) f yx(0,0) Let

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Q: (a) Find the critical point of f(r, y) = (4x² – 3) (2² + 43y). (x, y) (b) Find the discriminant,…

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Q: Let f (x, y) = r³ + y? – critical points of f . 4xy + 3x + 2y+5. Find and classify all

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Q: The antiderivative of the function f(r) = 2.5 .0+7.3z is %3D -2.5 + 1.8z +c -2.5 0+1.8z+ c 6. -2.5…

A: We will integrate the function and use c as the constant of integration.

Q: Find fzyz. f (x, y, z) = x°y°z° + xy° + y°z %3D 6-

A:

Q: f(x,y) = x2 + 2xy - y? is an example of homogeneous function. OTRUE O FALSE TRUE FALSE

A:

Q: OFind the linearization L (1, y) of the function f (z, y) = /176 – 4,' - 16y at %3D L (z, y) = Note:…

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Q: [2xy + yz (i) F(x,y, z) = x2 + xz with domain R³. || xY

A: “Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: x² +y² F(x,y) = is a homogeneous function of degree x- y

A: We have to find the degree of the homogeneous function

Q: For the function: f (x, y) = In(x + 2y) + Find the linearization L(x, y) of the function at the…

A: According to the given information, consider the given function.

Q: maximize f(x,y)=xy subject to the contraint 6x+y=18  the last question is what is the maximum valye…

A: max . fx,y=xyS.t 6x+y = 18     6x+y=18⇒ 6x+y-18=0∴ gx,y=6x+y-18=0    Fx,y,L=fx,y-L g x,y⇒…

Q: xY 2. (a) Prove that the function f(x, y) is differentiable everywhere in its do- %3D x2 + y? main.

A: Solution is given below:

Q: 3. Find V x F for F(x, y, z) = -xZ x² + y² i+ -yz x² + y² =j+ x² + y²k.

A:

Q: Find the linearization L(x.y) of the function f(x.y) = 2x- 7y + 3 at the points (0,0) and (1,1). The…

A: f(x,y)= 2x-7y+3 fx  = 2 fy = -7 The linearization of a function f(x,y) at (a,b) is given by L(x,y) =…

Q: f(z) = (x²+y)+i(y²-x) is analytic %3D

A: We have, fz=x2+y+iy2-x Compare the equation with fz=u+iv we will get u=x2+y and v=y2-x Now,…

Q: Q.1 The natural domain of fur f(x,y) = lnx² + Iny is а) {(х, у):х > 0, у > 0}

A: Log function is defined for positive values

Q: The Linear approximation (linearization) of f(x) = at x = 2 is %3D (A) y3D -류(z-1) (B) y = - (x – 2)…

A: Given

Q: The Linear approximation (linearization) of f(x) = at æ = 2 is 1 %3D %3D (A) y = - (B) y = - (x – 2)…

A:

Q: Discriminant f(x, y) = 2 4 1 = of a function f(x, y) is defined as D = fxx fyy-fy. If 2x² + 2xy + y²…

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Q: Find df/dt using the chain rule and direct substitution. f(x,y) = squareroot(x2 + y2) , where y =…

A: Given f(x,y)=x2+y2   andy=t2  ,  x=t

Q: b) Let X₁, X₂, Xn-f(x) = {0x-(0*) x>1 e. w. find Suff. Comp. St.

A: Given that

Q: © f(X,y) = x4 + 'onY -10 © w = x*y - 10yZ z³ + 43X – 7tan (4Y)

A: It is partial derivative

Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.