y(x, t) Аехр(i(-kx? + ot)) II

Q: y = = Vx, 1s xS 8 Intograte ith

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Q: Find curl (3z i + 4x j + 9y k). curl (3z i + 4x j + 9y k) = ( i )i + ( i

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Q: Use chain Rule to find for 2. y = . +x²+x+1 I.W | 3. y = estn 3x Н.W

A: We have to find dydx using chain rule for the given function: 2.  y=1x3+x2+x+13.  y=esin 3x We know…

Q: 4-у2 r2x+y dzdædy -V4-y2 Jo

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Q: ☺ cosh"z= Loy {2+/2

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Q: 1 dz (z + 1)°(2:² + 4z – 34)i

A: Solve, as follows:

Q: Use Cramer's rule to solve for r' and y in terms of x and y: y = 31' – 2y

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Q: Evaluate the integrals

A: Disclaimer: Since you have asked multiple questions; we will solve the first question for you. If…

Q: ux.ュメトXス1いスコ-Y Palx, utェッズ)-。 入2コメ; +メュ-」+5- メレ 2 d、しズuメッ]= xit Xzメ]-6 fnd in Ganeral rm.

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Q: 5-4y2 dy 3+2y

A: To evaluate ∫5-4y23+2ydy

Q: f (x, y) = 169 x² + y² at (-3,2).

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Q: 2) y' – (cotx)y = -(2cosx)y2 %3D

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Q: The Cornev 8-I make outbound A, B. 3. achieve Ax-u38/--12A.B %3D Otrue 2)Err

A: We know that  a×b represent vector product of two vector a and b  a.b represent scalar product of…

Q: What is the counterexample of x+x>x ?

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

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

Q: (t + 2)°y" + 3(t + 2)y' +y= 0, 1>-2, V1 = (t+ 2)

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Q: mTQ = %3D mQR = %3D U 44 mTS %3D T. R 25 MSQR %3D MRQT %3D

A: Problem 1   Problem 2

Q: TF x and y are orthon ormal rectors then Pind Value of Ilx+y12 - ||x-Y2

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Q: 2ryy' –1-y - 0, y(1) = 2, one can fir

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Q: x = 2 + 3t, y = cosh 3t , 0 <y<1

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Q: max z = 2x + 8y %3D s.t 3x + 9y 12 х, у > 0

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Q: 2. T1: R2 - R2, T1(x, y) = (x – 2y, 5x + 2y) T2: R2 - R2, T2(x, y) = (0, x)

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Q: (2-x²) y" + 2xy' - 2y = 0 olution to

A: Given differential equation is 2−x2y''+2xy'−2y=0.....1. a We have to verify that y=x is a solution…

Q: Y1 (t) = 2t – 3, y2(t) = t² + 1, y3 = 2t² – t, y4 = t² +t +1 %3D

A: We will find out the required solution.

Q: This question is from partial differential equation please sir g give me answer immediately

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Q: Solve Ut = Urx, x > 0, t> 0, u (x, 0) = f (x), u (0, t) = 0.

A: Given partial differential equation isut=uxx,     x&gt;0,     t&gt;0ux, 0=fxu0, t=0

Q: f (x, y, z) = x4 – 6xy? + 72% - (x, y, z) → (0, 0, 0)?

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Q: [₂ x³ √√x² +1 3

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Q: (i) Find the covariance of Y1 and Y2, Cy, Y,

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Q: S(2y + 3)?/ y+ 2 dy

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Q: Solve by Chain Rule 8 poir f(y) = /2y + (3y+ 4y²)³ %3D

A: Here clearly not mentioned, what to do with this question, but as we know chain rule is applied to…

Q: Calculate y', y" and y" for y = . [Hint: y= r-le", product rule, several times.] use

A: Topic  - differentiation by parts

Q: Find fxy(x,y) if f(x,y)= e 8xy² fxy(x,y)=

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Q: xyz 9. f(x, y, z) = x² + y2 + z2

A: Givenf(x,y,z)=xyzx2+y2+z2To find Domain of above functions

Q: d²y Given that x3 + y³ = 2, prove that 4x dx² y5

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Q: Find fxy(x,y) if f(x,y) = (x² + y²) 7. fxy(x,y) = ...

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Q: dy If dz 3x - 3 and y(0) = 8, then y(1) %3D ---

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Q: d³y of y = (3x*-5)(2x³+9x-6) Determine the %3D dx3 7x5

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Q: af(x,yz) -

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Q: Lion 1-y If x = Show that 1+y dy V1-y

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Q: af Find y dy √y+2 using the substitution u +5=√√y+2.

A: Follow the procedure given below.

Q: Dketch a 3-dhensranal grapn of the equetey 1巻)Z-6-2ーy2 ×Z0 42O 2) 0-

A: 1) given equation to draw the graph is z=16-x2-y2 ,x≥0,y≥0 since x,y are positive the graph will be…

Q: V1. y=x' +1, the axes, x=3; 0X 1 y =-, , y-axis , y=1 & y =3 ; OY

A: Here we have to find the volume.

Q: I Y=t5メPYove th y-2(21くるど

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Q: 20TH MAHH, Determine The deriva )y=3e* +916 4x t I +

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Q: Use Example 4 to calculate -(r x r'), where r(t) = {t, t2 , et)

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Q: Q.2 R ex2-2 dxdy, where R between x = -y, y = 0 and x = -! -3, y = -9

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Q: d²y If dx2 -n?sinnx , (y" = 0,y = 0 when x = 0), then: %3D

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Q: f(x,y) = /² + y?

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Q: 33) - 2y + y, + y; = 0, y + y', = 4t +2, y, (0) = y, (0) = y,(0) = 0 y + y, = t² +2

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