[2x²ydx +xyd es (0, 0), (2, 2) a

Q: 3tan z sec? x dr 2.

A:

Q: find ƒx , ƒy , and ƒz . ƒ(x, y, z) = 1 + xy2 - 2z2

A:

Q: T(x,y, z) = x² + 2y² + z

A:

Q: If f(x,y) = x In(2y³ – 5) + y e* , find ! of and ôx ây

A:

Q: Find the value of c such that S xe = 3.

A:

Q: find ƒx , ƒy , and ƒz . ƒ(x, y, z) = (x2 + y2 + z2)-1/2

A: Differentiating with respect to x, keeping y and z as constants, we get

Q: Find ∇2f, given that f(x, y, z) = 1 / (x2 + y2 + z2)1/2.

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Q: f(x) = In(2x) %3D (x), %3D

A:

Q: (c) Show that V(3) = o²(X'V-¹X)-¹.

A: 3. c From the given information, y=Xβ+ε Eε=0, Vε=σ2V From the part b, β^=X'V-1X-1X'V-1y

Q: Sketch Z= 2x^2 + 3y^3

A: Given, Z=2x2+3y3 To find: Sketch the plot for Z

Q: (a) Find x, y el such that x+y || x || .. = 1 = || y || = || ** ||**y. ∞o 2

A:

Q: Find x and y in terms of a. X + y = 0 х+ ay %3D 6 (а + 1) (х, у) —

A: Given:    x + y =0        --------1   x + ay = 6     --------2 from 1: x = -y put the value of x in…

Q: Find ƒyxyz if ƒ(x, y, z) = 1 - 2xy2z + x2y.

A: Given that, fx, y, z=1-2xy2z+x2y           ...(1)

Q: Determine if the nontsivial Soluton ystem has a X,-3>c + 7)C3=O -2x,+ Xz -4x3=0 923=0 Xi + 2x2 +

A: To determine if the system has a non trivial solution.

Q: - If y = e3x and y = e-3x , prove that: - %3D d²y 9y = 0 dx2

A: Given: y=e3x⇒dydx=ddxe3x⇒dydx=3e3xNow,d2ydx2=ddxdydx       =ddx3e3x       =3ddxe3x       =33e3x…

Q: af Given f(x, y) = In(7x² + 9y²) then

A:

Q: Let F(x,y) = (3x +4xy)i + (2x² -y³j

A: Given,

Q: Find f, and f, for f(x, y) = 12(6x-3y +8)°. %3D 1,(x.y) = %3D

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Q: f(z) =z2 is discontinuous in C

A:

Q: Suppose that a = xdy is a 1 form and Y(v1, v2, v3) = ((v1 – v3)² (v2 – v3)²) ædy what is "a ?

A: Given α=xdy-----(i)γ(v1,v2,v3)=((v1-v3)2,(v2-v3)2)---(ii) To find γ*α------(iii) from (ii) we…

Q: r²[(x²-y²)²] 1²₂5²² du dt x+y

A:

Q: 24. f(x, y) = In(x² + y)

A:

Q: If f(x, y) = 8xe2y + 8y Inx, then is given by:

A: The given function is: f(x,y)=8xe2y+8y ln x Now, ∂f∂x=∂∂x8xe2y+8y ln x       =8e2y+8yx

Q: 1 of f(z): is z2+2z+2 %3D

A:

Q: Calculate the LOS of y = -x² + 2x + 4 LOS is x = a is b is ,c is

A: We have to find the line of symmetry and values of a, b, c in the given question.

Q: Making use of the fact that ˆα = y − βˆx and βˆ = SxySxx, show thatni=1[yi − (αˆ + βˆxi)] 2 = Syy −…

A: Given

Q: Z = X, + X, + at X1, X2. are NC

A: We are given,  X1, X2... are independent random variables with E Xn=mn  and N∈P0(λ). The set is…

Q: Evaluate the Cauchy principal value of 2x² - 1 fo dx. x4 + 5x² + 4

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Q: Let f(x,y) = 10x^3y^4+ 21xy^2 Find ?yyy

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Q: 3. y = x³ – 3(x² + w²) 4. y = x7 + V7x - 1 TT + 1

A: Differentiation wrt x

Q: 3. Given z =, show that ху xy(zxx + Zyy) уз — х3 2 || x²y2

A: δwδt=δwδxδxδt+δwδyδyδt+δwδzδzδt       =ysin(z2).(-1)+xsin(z2).0+2xyzcos(z2)(2t)

Q: Evaluate [ T 1-x² x² + y² dydx.

A:

Q: Find the domain of y = vx+6. %3D 12. O x 2 6 O x > 6 1/6

A:

Q: (c) Show that |(−1,1)| = |R|, where (−1, 1) = {x € R : −1 < x < 1}.

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Q: F(x,y, z) = 5x² + 2y² + 4xy + xz

A:

Q: 3 a AB: 4x + 5y = 13; midpoint (2, 1)

A: The equation of the line is 4x+5y=13. The midpoint of the line is 2, 1.

Q: 2s f( 8ts“, ), (x, 9) = 7xy, and af af ;(x, y) : Assume that w= Find and ds %3|

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Q: 2. y(x) = C1sin2x + C2cos2x + 1; y) = 0 and y' ) = v2 C1 = C2

A:

Q: Q- show that yo+(?) sy + (2) B²y_₁ = y + (1) DY...+ (1²¹) Ay -

A:

Q: Determine c1 and c2 so that y(x) = c1 e^2x + c2 e^x + 2sin x will satisfy the conditions y(0) = 0…

A: NOTE: Refresh your page if you can't see any equations. . the given solution is…

Q: Find those constants a, b, c, d such that f(z) = ax² + bxy + y² + i(x² + cxy + dy?)

A: The given function is : fz=ax2+bxy+y2+i(x2+cxy+dy2)

Q: əz əz +y show that x 3z x²y2 B. If z əx ду %| x+y’

A: B). From the given function: z=x2y2x+y And x∂z∂x+y∂z∂y=3z As we know that the Quotient rule:…

Q: Sketch Z= 2x^2+3y^2

A: To sketch: Z=2x2+3y2.

Q: Express.  y=√(3x²-9)  as a composition of u(x)=√x , v(x)= (x)² , j(x)=3x-9

A:

Q: Evaluate /, a Te dydx y2 2 JJ4X-x² 32 dydx (x²+y²)' V4x-x? O 4 In(v2 – 1) – 4+7y/2 3 4 In(v2 + 1) –…

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Q: A 3 X Y- X Y = 4xソーメニ2findr 3D2 and X"at X =1

A: Using definition of differentiation

Q: A- If y = e3x and y = e-3x , prove that: - d²y - 9y = 0 - dx2

A:

Q: f(z) =z? is discontinuous

A: f(z)= z2 is a polynomial function in z and polynomials are continuous everywhere.