Lt² V4-t² dt V(4-x)/(2\x) x(4-x)

Q: y= cosV1- x y' = V1-x² ² y' = 2v1- x² y' = 2va- x2 y' = Vx-x* 1 y' = 2Vx-x2

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Q: 13. y = x'/9, 0 sxs 2; x-axis

A: The formula for area of revolution of a curve on interval [a,b] about x-axis is given as…

Q: (a) 3 Differentiate y= y 3= us ing first principle. 2x+2

A: we are allow to do one question at a time  if you rest of answere please specify that part and…

Q: Determine la solución general de la ecuación diferencial Y'-2x/2-x^2(y)=e^x. Y(2)=4

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Q: 2 √2x-x² SJ J² J²^ √√√x² + y² + 2 00 y²)[2x − (x² + y²)]dydx -

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Q: Metodo de coeficientes indeterminados 3y´´-2y´-y=x^2+3x-6     y(0)=0    y´(0)=0

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Q: Obtain the general solution using variation of parameters y''+y = (csc³x) (cotx)

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Q: (ost) X= 3サ-3 DiD X-2-2y ¥ーにh で3,0) D3 Dy メーと2 サ=スメート X-4 <-リ-3 toノー4)

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Q: Differenitate: y = esin (z²+2z)

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Q: x = 4 y = x' |(2, 8) y = 8 y = Vx (4, 2) Figuro 1

A: Solution for question a: In figure 1 the region is bounded x=y2,the x-axis, where 0≤y≤2 The formula…

Q: 8z + 129z -) dr = (Use Term by term integration)

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Q: find dy/dx

A: Known formula: ddx∫rxqxftdt=fqx q'x-frx r'x.

Q: Integrate: 2dx + C of

A: The given integral is ∫6xx-2dx

Q: Expand completely. (3z 1) ar + ba + cr+ da² + ex + ƒ %3D d = and f=

A: Given 3x-15=ax5+bx4+cx3+dx2+ex+f To do  Find the value of a, b, c ,d ,e and f in the expansion

Q: dt dt '3 -1 C. X' =1 X+2 Je5t (undetermined coefficient).. 1 -1

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Q: Yuz - xUy = 0, %3D

A: Find out for each of the given initial conditions whether the problem is solvable or not. Then find…

Q: Vx2 +1 – Vx² – 1 y = Vx² +1+ vx² – 1 2.x3 dy = 2x - d.x - - show that Vx4 – 1 -

A: Given: y=x2+1-x2-1x2+1+x2-1      ......(1) To Prove:  dydx=2x-2x3x4-1      ......(2)

Q: Max Z = 4X1+10X2 %3D s.t. 5X1+4X2 < 200 X1+2X2 s 50 X1+X2 s 20 X1, X2 0

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Q: Evaluate: ₁²-du So -3 (x² y²)²7 x+y du dt

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Q: (2) Find dt2 if y = x2 + 3x -7 and x 2t + 1 | 2

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

Q: V2x-x2 SS2*-*" (x² + y²) dydx

A: Changing cartesian to polar coordinates: x2+y2=r2x=rcos θy= rsin θ x ranges from 0 to 2y ranges from…

Q: Solve using D-Operator 3. y + 2y + y = x²

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Q: [₂ x³ √√x² +1 3

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Q: x^2=Axy+By

A: Simple value put

Q: Differentiate. ' a) y = 2cos(x²)

A: Hi, at a time we can answer only one question and the exact one was not specified. So, I have…

Q: Differentiate: y = 4cos (-)

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Q: y = sec* ( Vsin(2t)) sec³ 3.

A: The objective is to find the derivative.

Q: 4+°メ -> X-X %3D dt メ+3

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Q: Solve y(x)=1–2x–4x² +[3+6(x-1)-4(x-1)ʻ]y(t)dt it.

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Q: 7x-4y-3z = 21 -4x+7y-z = 0 -3x-y+5z = 0 x, y, z?

A: Given

Q: 33. V2m – 1+2= m 34. V2x + 9 = VT + 3 35. Vē + V1- e = 1

A: 33. The given equation is, 2m-1+2=m

Q: Q-3- Eilaluate #the fallowing Integration x²-1 x² 1- x3 2 2.

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Q: suonenba 5x mons: (1) +- = 3x + 3 (ii) x + 7x + 12 = 0 In (x +4)- In (x*) = 4 = 15 (iii) %3D (iv)…

A: Simplification

Q: S sec 2ydy

A: Topic:- integration

Q: .3 1+ at dt

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Q: Solid inside x2 + y2 + z2 = 16 and outside z = √x2 + y2

A: Given:

Q: dt 2 (t–1)(t²–1)²

A: By using partial fraction we can find the given integral

Q: y= cot(-2x) y4 3 12T 37 -1- -2+ -3+

A: We have to find

Q: (1 - V2) dt 44. 46. (2z – 3) dz - 3

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Q: 6) qyo -x² +2x + S%y +62=0 sty

A: 6)

Q: hich vect וdtiolו y and 2? 1 -2 y = 1 -6 x = 2 8 -1 2 -1 5 2 -3 [ 2 -1

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Q: Evaluate. 2t 2t dt%3D

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Q: y = Vx – 4 А. Domain: х > 4 Range : y 0 Range : y > –4 D. Domain: х > 4 Range : y > 0

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Q: x2 - y2 + 2Cx = 0

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Q: find orthogonal trajectories of   x2+(y-c)2=c2.

A: x2+(y-c)2=c2 now differentiating both side with respect x , we get 2x+2(y-c)dydx=0 or, dydx= -x(y-c)…

Q: 1/V3 :-1 1. dt 4 A - 1

A: Solve following indefinite integral: Factorize the denominator Cancel similar factors: Now…

Q: Vt3 e-st dt 4s2

A: Explanation of the answer is as follows