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Q: 3 wu= 2-x. [ w/2-xdx= If U = | x/2-x dx= 3 (2 – u)Jūdu Luūdu -1 .3 uſudu D (2 – u)Vūdu -1

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Q: (11) Evaluate [[3x+5y+i(x²-y') dz along y=x (0,0)

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Q: dy (2) Find at x =-1 if y = u³ + 5u – 4 and u = x2 + x dx

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Q: dy 2ty ii) 12+1 - 21 – (2 – In(t² +1)) = 0; y(5) = 0

A: Differential equation of the form Mdx+Ndy=0 is said to be exact if ∂M∂y=∂N∂x Given differential…

Q: die ktvaate et:rlrs erziv. 2l y=a* + &r-- 5+e" Kl) =

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Q: (2xy+ 3x2)e, +(x² – 2yz + 2y)e,- (e2 + y?)e, olan f(x, y, z)

A: Given that the function is

Q: 3. ex In y dy – y e` dr = 0 2 (In y) In y + e* = c In y - e+1 2 (In y)- e* = c

A: See the details solution in below

Q: Q.6 Show that: X-1 X+ y – 1(x-1y)= B(x,y)

A: In the given problem we have to show that                                 x-1x+y-1β(x-1,y)=β(x,y)

Q: kx 4+x² If k 1, evaluate k (a) 2 kx (b) 2 J₁ arctan (2x) + C arctan (2x) + C dx. (c) // ln(x² + 4) +…

A: Given: ∫kx4+x2dx We have to evaluate the given integral.

Q: (1) E(x, -x)² =Ex} – nx² | (ii) E(x, –x)(y; -y)=Lx,y, – nxy (üi) E(x, – x)(y, – F) =Ex,(v, - )

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Q: f(x)= (ex+2 +1/e-x -14ex+1) / (xex-ex/x+1 +lnee^x) differentiate?

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Q: de (x+2) h+2+ +C (r+2) x + 2- Option 1 Option 2 In Ix + 21 + 4r+5 + C in x + 2 (e+2) O Option 3…

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Q: u(2) 8, u (2) = 2, v(2) = -2, v '(2) = -4. %3D %3D at x = 2 dx 9. O 16 7. O16 7. 16

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Q: 21 11 f(x) dæ f(x) dx f(x) dx - 8, where a = and b ...

A: The given integral equation is ∫821fxdx-∫811fxdx=∫abfxdx.

Q: 2. [f 5y ey dA, F- {(x, y): 0 s x s y?, 0 s ys 2} F

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Q: (1)F (s)= s +9 2s2 +s -1 %3D

A: Given: L-1s+92s2+s-1

Q: 2 2 Va? +x + Va? -x² If y = Ja? +x? - Va .2 Show that dy 2a 1+ 2 a? dx 3 Va* – x*

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Q: Find  y(4) (the fourth derivtive of y with respect to x) x2 - xy + y2 = 3

A: Given: x2-xy+y2=3 We have to find the fourth derivative of the given equation. The product rule of…

Q: F(S): (s+2)CS+1)(S-3)

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Q: 4) f(x) = ex – x, -5 s x s 2

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Q: L(cosh 4t) = %3D .a s²-16 .b O s2 – 8 .cO s²+16 S

A: option :- a

Q: dy 2. if y = In(x² + 1) Then at x=1 %3D dx 2- 2 In 2 2- 1 1- 4- 1/2

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Q: 2 (b) S(2 + tan (0))do (c) S 2'(1 + 5')dt

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Q: -1 Ans. f. = Tx+ y}, (r+y} -1 5) f(x, y) =- x+y

A: Since you have posted multiple questions, we will solve only first question for you. To getremaining…

Q: 2 O Finel F.S For Fex) = 2くxくだ 7. %3D 2. -2 37 2 2.

A: By Bartleby policy I have to solve first question, as these are all unrelated problems. These are…

Q: Ax) %3D х* — Лх2 - 12x where A> = > — Лх? — ЛЕx where ^> v that fis one-to-one on S = [- rmine f(S).…

A: Given, fx=x3-λx2-λ2x,  λ>0

Q: Fird XCK) is X(2) = 2くz-)(マ-3) Ans; SC) ャu(k)+と)uck)

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Q: 10 Let y = ( 2x + Then -A(2x + 10)" (2- 10)°, dy = A[ 2x + 2 - where A = %3D C = %3D

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Q: Find the function y(x) satisfying -8/9 = 6x dx and y(-1) = - 4. dy :-8/9 The function y(x)…

A: Integrate the equation dydx=6x-8/9 with respect to x.…

Q: dx using miscellaneous substitution will yield to secx + 1 Transforming S Ⓒ √ ²² +²2 dz (Α) -z²…

A: This question can be solved by substituting z=tanx2

Q: 2. f(x,y) = x5 In(y)

A: Given function is fx,y=x5lny. To find the first and second order partial derivative of the given…

Q: 5. Exact Diffe re ntial Equation: x(3xy – 4y' +6}dx+(x' – 6x² y² -1dy =0

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Q: 3t when LI 1 ニe then L %3D S- 3 S-3

A: If Laplace transform of the function f(t) is denoted by Lf(t) or F(s), then the Laplace inverse of…

Q: TVy+1-2 dy can be evaluated conveniently if we let x=VVy+1-2 and dy = 4x(x² +2)dx. T True F False

A: follow next step

Q: f(x) = 3a + 57a2 + 357x + 735 %3D O as x 0, y 0 and as x 0, y ∞ - as x 00, y → 0o and as x -00, y -0…

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Q: .7 f(x)dx= 12 and f(x)dx = 3.1, then 5. If %3D

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Q: 2 sec 0 r drde = x² + y² dydx %3D 0. True False Reset Selection

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Q: dy — 2х — сosX + e-2х dx 2 TT 1. Given that and y = 1 when x = 5. Express y completely in 2 terms of…

A: Topic - differential equation

Q: S-ydx + xd - ydx + xdy, C: y² = 3x from (3,3) to (0,0) O 4 O O 2

A: Solution is given below:

Q: EX~U(0,1) if Y= =L l(t-x)~ Exporential (A,

A: From the given information, X~U0,1 The probability density function for X is, f(x)=11-0       =1,…

Q: 2. y" - y = x, y(0) = 1, y'(0) = −2, h = 0.1 from x = 0 to 1.

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Q: 3 9-r22 1 dy dz dr 9-r2 0_æ²_22 (x² + y² + z²)1/2

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Q: 73.xy-z(x- y)' (19)

A: 73 Given expression is xy−zx−y2. We have to find the value of the given expression x=3, y=-2 and…

Q: どa (en) (2-x)8 y = X+7 FiNo dy

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Q: 2s+2 ds = In|s| – In\s + 2| + C %3D s3 +3s2+2s

A: Here, we are solving only 1st question and for the remaining question post the question again.…

Q: go SL x* dy- dy ax where L is segmeut bekueeu two pailuts (9,0) aud (1,0)

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Q: -a+ito + DNE - 十→f -2 1 DNE + DNE - -1 DNE DNE | -1 1 2.

A: The function f is increasing on some interval, if f'>0 on that interval.    The function f is…

Q: seParable 5い / / とll y=2メJタ! 4 xx

A: