O foxy) = senx + seny + Sen(xg) t1 %3D 2 fcxry) = xe y concet)t 8x

Q: | 21×VX2 + 1 dx = 14 2- 7, what is 21uV u2 + 1 du? Given that %3D

A: The properties of definite integral is ∫abf(x)dx=-∫baf(x)dx. Use the property of definite integral…

Q: 5. If u = e1#1+az#2++anIn, where a² + a³ + · ·..+ a = 1, show %3D + = U dx?

A:

Q: dt (e2t + 8et + 7)ā et+4 a) 9ezt +8et+7 +C b) In(e2t + 8et + 7) + c 2 c) 5Ve2t+8e*+7 +c e4t d)…

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Q: if y = secx prove that y^2+y=2y^3

A: Equation relates the number of variables combined together by algebraic entities using equality…

Q: 2. Evaluate f. (y²dx + x?dy) where C is the triangle with vertices (1, 0), (1, 1), (0, 0).

A:

Q: aw Find ду if w = z³(In(zy))(e**y*z*) %3D

A: Given,        w=z3ln(zy)ex2y3z4

Q: Give an e xam Ple of (T, m') ameasurable SPa ce F; x → T {E & CX : fCE) ET3 m is not

A: Given, Τ, m a mesurable space fi:X→Τ , m=E⊆X: f(E)∈Τm is not a σ-algebra on X.

Q: 7. Show for y = u.v that y"= uv"' + 3u' v'" + 3u" v' + u''' v.

A: The detailed solution is as follows below:

Q: 4 - If w = x + 2y + z? , x =, y= r2 + In(s) , and z = 2r aw find at the point (r, s) = (-8,4). as…

A: See the attachment

Q: Let -2xy – 3yz – cz, x = st, y= e", z=t? Compute ди (4,-5) = ds dw (4,-5) =

A: The given function.

Q: 12. Calculate the area and volume of a sphere knowing that the length of its equator is L = 12p cm.

A:

Q: af Given f(x, y) = In(7x² + 9y²) then

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Q: dy let y = xtan z then is da elect

A:

Q: A- If y = e3x and y = e-3x , prove that: - d²y dx2 – 9y = 0

A: The solution for the above question is as shown below.

Q: Show that d(y,u)/dv = (1– v²/c)3? for y, = 1//1- v²/c?. %3D

A: Given: γv = 1/1 - v2/c2

Q: show that Ф (x, y, z) = аф PDE : агф дуг + дуг I х2 +у2 +Z2 024 072 satisfies the

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Q: (b) Compute r if: arctan r + arctan 1 = 2 ( arctan z arctan

A: tan-1x+tan-11=2tan-1x-tan-113

Q: af (2,0) ay f(x, y) 3D хетУ + 5у%; af (2, 0) = Əy

A:

Q: A If w= f (x, y), where x = rcos 0 and y = rsin 0 , show that 2 1 + 2 +

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Q: s) Given u(r, s) =r2 - 2s2, wheter= and s = y? - r, compute for du

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Q: 9. If y = V-|x|, then Dr = %3D %3D

A: Df :  Domain of function f  The set of all input values where f defined

Q: 3. Show that S, has the presentation (x, ylx* = y? (xy) %3D %3D

A: Given: Group S4 We need to show that S4 has representationx,y|x4=y2=xy3=1

Q: Making use of the fact that ˆα = y − βˆx and βˆ = SxySxx, show thatni=1[yi − (αˆ + βˆxi)] 2 = Syy −…

A: Given

Q: Determine Dariuior souHon 2y"+ Sy't 3y •0 : y(O) = 3 , y'C6) •z

A:

Q: Find and when (TU – V)² In(W – UV) = In(2) at the point (T, U, V, W) = (1, 1, 2, 4).

A:

Q: Q1 but f(x,y) = x²y²sin-'O xf, + yfy = 4f (x,y) between

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Q: 63. r(и, v) %3D Зи сos vi + Зи sin vj + 18u'k ||

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Q: Show that Z, dv=2010 %3D if B= 2) : -1 Śn s3, ISySY,e

A:

Q: O Evaluate the foll owing in tegrals: Ins 2x+y (Sinztcany) dx dy In2 e dydx JA ROSISu, Isys2

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

Q: Let z = 6exv , find dz %3D

A:

Q: In Exercises 53-58, compute the derivatives indicated.

A: Here given as fx, y=3x2y-6xy4 Now ∂f∂x=∂∂x3x2y-6xy4=6xy-6y4∂2f∂x2=∂∂x6xy-6y4⇒∂2f∂x2=6y

Q: 3. Assume that z= 2(r.y) and ee = ryz Find and

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Q: if y=Asinx+Bcosx then prove d2y/dx2+y=0

A: Given,

Q: 4) Lett =,u = x? - y² ,v = 4xy³. Find %3D ax ду

A: t=uv

Q: 2s f( 8ts“, ), (x, 9) = 7xy, and af af ;(x, y) : Assume that w= Find and ds %3|

A:

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: O The madices of cervadere af r= éat any poind Y, is (@) r?VTt (b) rvite? (C) Vitaž (d)

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Q: Given f(z, y, z) = /1z2 + 3y? + 222, find %3D f-(z, y, 2) =| f,(z, y, 2) = f.(z, y, z) =

A:

Q: If ø(x, y, z) = ry²z find grad ø at (2, – 1, 3).

A:

Q: Q- show that yo+(?) sy + (2) B²y_₁ = y + (1) DY...+ (1²¹) Ay -

A:

Q: Let w = 4x? + y? + z? x = psinpcose y= psinpstno z = pcoso Find dw dw dw de ee de

A:

Q: (b) ƒ(x, y) = Vy – x · In (y+x) -

A: Given (b) f(x,y)=y-x ln (y+x)

Q: - a. ARWZ W WZ RW b. ? ZR %3D c. RW = 15, ZR = 10, and SZ = 8. WZ 2 and RS = ? R

A: Given, ∠WRZ=∠WZS

Q: Given that z = f (u,v), u=x + y and v = 2x - 2y. Show that 4. дхду ди?

A:

Q: BeR NOULLI 's EQUOTION (2yーX)d水+ラ×ydy:o ソ+PCx)yq(x) yh XrlwDepenとn 3 y= Depen Dest

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Q: xlet X,Y,7 be v.V.J with Joint fA くれく くらくtyerzc

A: The joint probability density function is given to us the conditions on x, y, z are also given to…

Q: 2. Given z = , show that ху xy(zxx + Zyy) 2 y - x3 x²y? |

A: Function is the unique relation where each x is mapped to unique y. It can be of many type,…

Q: Which condition would prove AJKL - AXYZ? K Y 56 7. JL XZ 造=8 KL 8 JK %3D XY

A: We have to find which condition would prove ∆JKL~∆XYZ.