1on to ove tha (X +Y)(X + Y) =X

Q: az xdz + Y- = xy+z. a) If z = xy - xei , show that x- ду

A: Since you have posted multiple questions in this question which are not interlinked so I have solved…

Q: Juneten and be fure at lebel aut least thre f (n) : Su

A: As asked we can find the answer as below

Q: sn'x プェ Sec'x-1 from [o, of 2.

A:

Q: 1 x*y" + xy' – y = In x; yı = x – In x, y2 = ' - Inx

A: Given the Cauchy-Euler differential equation             x2y''+xy'-y=ln x Solve it.

Q: 7. Evaluate the Integral S (x + 3) dx

A:

Q: b 1+ e2x Evaluate the integral. ex xp 1 + e2x

A: Given that: ∫01ex1+e2xdx

Q: 14. Evaluate the integral. 4 (y - 2)(2y + 1) dy

A: Given that : The integral is ∫04 ( y - 2) ( 2y +1) dy

Q: .'( , "ג oa3 (125x*y)" 学 A: 125 2 3 $%% 1/3 5メ Y C: D: VONE OF THESE

A: Since you have asked multiple questions in a single request, we would be answering only the first…

Q: 2. given that y = 0 at r=1

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Q: 1-y² L In (r* + y? +

A: Introduction: The process of determining the area of the region under the curve is known as…

Q: 7 y=tanx show thats y" = -2Siny cosy 1f y=e Snbx show that:

A: Dear Student, according to the Bartleby guidelines, we can answer only first question if multiple…

Q: y If z = show that = 0. x + y?*

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Q: 13. the , xydA, where ySxsy?}

A: First I have set the limiting double integral from given information and then solved it .Final…

Q: Is it possible to find a number  n  such that is ∫0∞  xn dxconvergent?

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Q: 2. If z = x° In 2.xy, find at 1,-

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Q: (a) Evaluate the integral ſ x e2x çdx (2x+1)²

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Q: dy Find Z for y = (8+ x³ In x)ª + e3x

A: We have to find out derivative

Q: 18. y = (In 0)" > dy de = T(In 0)-1) () T(In 6)(-1) %3D

A:

Q: 8. Evaluate the integral S xydx from x=3 to x=6 when x = 6cos0 and y = 2cose A. 9/7 B. 9/3 C. 5/3 D.…

A: Topic:- integration by substituting

Q: Prove by mathematical induetion. Ine I+2 +2+2 +2° = 2.

A:

Q: dx = O In|æ| + C O In(x) + C O z° + C O Does not exist.

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Q: 1. Find the interval(s) wheref(x) = xe6* is concave down, if such an interval exists.

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Q: -ALef xe Rbe Such thad Xn→x, show that Yn = xi %3D 4 X.

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Q: 2/3 Determine the length of x=| for 0<ys2. Assume that y is positive.

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Q: az Find for z = x'y'eV

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Q: Let z(x, y) = xe* + sin xy + y - In 2 then a a) -In 2-2 b) In 2-2 2 c) 2 (²-1) d) - 2 (²+1)

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Q: dy 3. Find dæ if y = In (aVæ +1).

A: Given,            y=lnx3x+1

Q: 1f itwas x25ect, yatunt prove Thut dy

A: Simple derivative

Q: az Find for z = x²y°e®Y dx

A: The given function z is zx,y=x2y2exy We have to find the partial derivative of z with respect to x.

Q: Find the derivVative of the function. 5. y= In 8v +5 dy dv %3D

A: The objective is to find the derivative of the function.

Q: ronskian of the DE : xp(x)y' + 3y = 0 = er² et? et?

A:

Q: X+ xy B. Evaluafe the tripe in tagral S5* xy dydzdx,

A: As we know that: The Power Rule: ∫xndx=xn+1n+1+C ; n≠-1 (B). From the given integration:…

Q: Eva 6 SSin'z osx dy

A: ∫undu=un+1n+1.     cos2x+sin2x = 1

Q: 4. Let z = x2 + y³, x = 2st, y = s - t2, s = u", and t = u sin w. Compute for Oz ду and дw ди

A: Let z=x2+y3, x=2st, y=s-t2, s=uw, and t=u sin w.To compute for ∂z∂w and ∂y∂u.

Q: of fxyl = 3X-y+6 Subjected QI Find to x+y=4 extrume v alues

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Q: dz Find if yz – In z = x + y ax

A: To find the partial derivative of z of yz-ln z=x+y with respect x, differentiate yz-ln z=x+y, while…

Q: S 1.Prove that L (coswt) = %3D s2+w2

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Q: 2): Consider the DE y" – y" – 6y = 0 -

A: Follow the procedure given below.

Q: 23. x*y" + xy' - y = In x

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Q: Evaluate the integral. 2 2 t+ dt 15 OA. 29 О В. 6

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Q: Q3/ prove fry = fyx if f(x,y) = x + xy – 5x³ + In(x2 + 1)

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Q: x2 1 dr dy = a° In(1+ x² + y? 3

A:

Q: Find y' if exy = e 4x -esy-

A: NOTE: Refresh your page if you can't see any equations. .

Q: 3. If f(x,y,z)= In 4 xyz Ite t3y:²s²) , find f,,f, and f..

A: Given that: f(x,y,z)=lnxyz4+e-(3xy2z2)

Q: (1,1) Evaluate [ (3x²+4xy+ix)´dz along y=x² (0,0)

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Q: RA Find dx dt x In(x) /1 + (In(x))²

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Q: S √x²-a² X dx

A: To solve the given integral.

Q: Evaluate xy dS. S: z = 3 – x – y, first octant

A: Given query is to find the double integral in first octane.