Q3) If f (x, y²) = x² + y² + Vxy find : af(x²y) %3D and (x2y) ax ду

Q: 6x2+7y2=C satisfies 6x+7yy' given the inital condition y=4 when x=6 what is C.

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Q: Q3) If f(x,y²) = x² + y² + vxy find : af (x²,y) and f(x²y) ax ду

A: A scalar function f(x,y) is a rule that is used to associate a number or quantity with a particular…

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

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Q: 3. f(x, y) = (3x - 5y)2 + e4x In(4y – 9) + %3D 135 x4

A: We know, ddxxn=nx(n-1)  , for any real number n. ddxln(x)=1x

Q: If f(x,y,z)=x²y³-y²z³ Then f;= -3y²z2 Jlgn

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Q: (B) let y = 3sin5x - 2cos5x show that ax y + 25y = 0

A: Given :y=3sin5x-2cos5x

Q: To the reci max z Ax1 +B x2 A=6 s.t. 2x +4x 2 12, B=1 -X1 + 2x2 S 2, X1 20, x2 Free.

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Q: compute ∫_D 2ydx+3xdy, where D is described by 0≤x≤1, 0≤y≤1

A: Green's Theorem: Let C be a positive oriented, smooth, simple closed curve. Let D be the region…

Q: 4. f(x, y) = 10x²y* – 6xy2 + 10x2; fx(x, y), fy(x, y) %3D -

A: Consider the given function as fx,y=10x2y4-6xy2+10x2

Q: Q4: If f (x,y,z) = x?y³ – y²z³ then fy = %3D -

A: Given,           fx,y,z=x2y3-y2z3

Q: Determine whether X and Y are independent: 2e--2y x, y > 0 a. fxy(x, y) =

A: Hello! As you have posted 2 different questions, we are answering the first question (4-2). In case…

Q: dz Find - if z = (9x + 5y)°. dy

A: we can find the derivative as below

Q: Right AXYZ with mZX XY = 12V2 Given: 45° and Find: XZ and YZ

A: Given a right angle triangle ∆XYZ and m∠X=45° and the adjacent length XY=122. To find XZ and YZ.

Q: Show that y" + ay' = b, wherein a and b are constants, can be reduced to y' =+C₁e-ax using 2…

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Q: for w = ze(zy²+2:). Do not include =" in your answer.

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Q: f(x, y) = In(4x + 3y) Calcule

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Q: f(x, y) = In(4x² - y) %3D

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Q: When x = 2s+7t, y=5st and z= 3.x2 – 3, in the form of s and t. express

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Q: (8) If w = 5x2 + 2y2, x -3s +t, and y s - 4t. %3D aw and at aw Find as

A: w=5x2+2y2,   x=-3s+t,  y=s-4t

Q: Зх — 4у + 23 (a) f(x, y, z) = '9 – x² – y² –. - V2t – 4 x² – y? - (b) g(x, y, t) : -

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Q: 4' for T- T2• T, and T- T1• T2. x - 5y, 4x + 2y) y, 0)

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Q: Find Duf at P. 2, -k 3' 2 f (x, y, z) = 6x³y°z°; P(2, – 2, 2); u = i+ 3 -

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Q: 2,t-3P dt, then %3D 12

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Q: ral soluion of qineral xy" + 2y'=6x Find the

A: We will first reduce the order of given differential equation

Q: Show that y" + ay' = b, wherein a and b are constants, can be reduced to y' =+ C₁e-ax using 2…

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Q: 9. If x2-xy + y2 = 3, find y' and y", %3D

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Q: f(z) dz = 4, then 2f(x) – z dz 13 If %3D =

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Q: If x + y + z = 12 & x² + y² + z² = 96 & !.!,!= 36 then value -+-+ -%3D X y of x³ + y3 + z³ is

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Q: Find Duf at P. 1 2. f (x, y, z) = 6x³y°z°; P(2, – 2, 2); u %3D - -

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Q: 3x + 11y af If f(x, y) = then is : 3x – 11y dy - 66x (3x + 11y)² 66x (3x – 11y)² 66x (3x + 11y)2 66x…

A: Partial derivative

Q: *宗+> B. If z = show that x 3z %3D x+y

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Q: Q2) Show that y = 35 x* – 30 x2 +3 satisfies ( 1- x² )y" – 2xy' + 20y = 0 %3D

A: y =35x4 - 30x2 +3 satisfy (1-x2)y" - 2xy' +20y =0 for this wew find  y" and y' y' = 140x3 - 60x y" =…

Q: Given f(x, y, z) = /2x – y – 5z, find - - f-(x, Y, z) = %3D f,(x, Y, 2) = %3D f-(x, Y, z) =

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Q: lf f(z, y) = 5ery + 1 sín (inr + y) + 2r + 3y, find-a-,-,-and

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Q: Prove if X,Z, y > 0 xy (3x +2y – 4z)+ yz(y+3z – 4x)+ xz(x+2z –- 4y)>0 then

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Q: 3. If V = (3r'y-1,x2'+y',-2r:"). Find grad divl at the points (2,-1,0).

A: We have to find grad(divV ) at (2,-1,0) where  V = (3x2y-z,xz3+y4,-2x3z2)

Q: In AXYZ, PQ I| XY.If XZ= 15, YZ= 12, and ZQ = 8, what is ZP?

A: given XZ=15, YZ=12, and ZQ=8What is ZP?

Q: f (x, y) = {* - kx(x — у),0 <x< 2,-х <у<х elsewhere

A: (i) Consider the property for a joint PDF, ∫-∞∞∫-∞∞fx,ydydx=1 Substitute the values,…

Q: Find Duf at P. 2 f(x, y, z) = 6x³y°z°; P(2, – 2, 2); u = ;i + -k

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Q: Find X only using Crammers rule 2x+リ-「Z=D2 x2 -y +VZ 2 x? +2y +VN= 4

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Q: e-", if 0 3,

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Q: 3. Find and at (0,0) where if (r, y) # (0,0) if (z, y) = (0,0) f(1, y) = Are they equal?

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Q: Suppose that z = f(x,y), find for 4 x²z* – 5yz³ + xy? - 3z? = x

A: Given: 4x2z4−5yz3+xy2−3z2=xz=f(x,y)∂z∂x=?

Q: Find all the local maxima, local minima, and saddle points of the functions in Exercises 11-20.

A: (10)Consider the provided function, fx,y=x2+2xy Find all the local maxima, local minima, and saddle…

Q: f (x, y, 2) = x³ /+42³y² – xyz +x² – Vz5 VI+ 42°y? – ryz+ x² – Vz5 - -

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Q: 6. Differentiate y with respect to x using A-method. x-3 a. y = X b. у %3D V4x + 3

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Q: If x &lt; 0 and y &gt; 0, determine the sign of the realnumber. xy

A: Let x&lt;0 and y&gt;0

Q: Q,3 Evaluate [II, xyz dxdydz, 3 < x S-2,0 < y S 1,0 S zs-

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Q: What is L[y] if y = u3(t) (t- 3)2? %3D L[y] = e3s . - 3 O Lly) = e3s. 2 L[y] = e-3s. 2 O Lly] = e-3s…

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