2. Find ( +x) dx, where B> 3. 27 a) 2 2 b) В2 + В— 12 27 c) 1 1 3 d) 12 – B² – B e) None of the above

Q: 10. If z = x + f(u), where u = xy, show that dz = x. х дх

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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…

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Q: Evaluate: S (In(2æ – 1) – (5) + 25 ) dx - Limits: [1, 6] Using Trapezoidal, n = 30

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Q: If z = In(x² – 2y), and x=u+v, y= e" , find and du If w=2xy'z', and y =x² +1, z= Vx, find dx

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Q: Given: z = x3 + xy", æ = uv + w°, y = u + ve" az when u = 3, v = – 2, w = 0 Find

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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: SL (e,9) f(x, y) = dx dy f(x, y) dy da 0. 0. 0. O True O False

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Q: 1 Evaluate J JA Totu2)2 dxdy, where A is determined by the conditions 1< x² + y? < 2.

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Q: If f(u, v, w) is differentiable and u = x - y, v = y - z, and w = z – x, show that fe af af + = 0.…

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Q: now if we take F (x, y) = (ax, ay), where a is any positive constan %3D

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Q: dv av and ду ди ди 2. suppose f(z) = u(x,y) + iv(x, y), show that əx %3D ду əx ||

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Q: Given f(x, y, 2) = In(x² + y? + z?), show that 2 dy? x² + y² + z²

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

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Q: How do I prove this?

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

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Q: 198). Let c be (,0) to(4r, 0,0) G=) ydx+ xdx t Xyz dz Is 6CX Y,Z) independent of C?

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Q: If z = xe, æe then dz = (e )dx + (ryev" )dy. Select one: OTrue OFalse

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Q: B. Verify if the relatin O y= xe is a səlution to yl-2y'ty =o. y = eco( 2x) is a solution to…

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Q: 10. If z = x + f(u), where u = xy, show that дz dz х дх = x. ду

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Q: Prove that c?p?-(jx² + jy²+jz³) is the invariant quantity equal to c?po?.

A: Consider the provided question,   Prove that c2ρ2-jx2+jy2+jz2 is the invariant quantity equal to…

Q: m+n If x"y" = (x+y)*** m, n d'y prove that = 0 .2 dx?

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

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Q: 2. Evaluateſff, y dV, where: E = {(x,y,z)|0 <x< 1,0 < y < 4x,y < z < x² + y} %3D

A: The solution are next step

Q: 3- prove that w comport dx =w dy yx 23 34 if w=: w = xy² + x³y² + x³y

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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: dæ is equivalent to Using the substitution u = x + 1 Vx + 1 1 -du 1/2 du du -1/2 du - 1) /u2

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Q: Given y = Va In æ , what is dy dr In z+2 In z+y7 dy dr dy dr In z-2 dy In z-I dr ||

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

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Q: Consider the formula A = Vx Vy.p(x,y) ^ ¬q(x, y). (b) Show that A is falsifiable (i.e. not valid) by…

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Q: (b) Let h(x, y, z) = x?y+ yz?, where a = u + v, y = u – v and z = -u. Calculate and ди dv

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Q: 2² dædydzB = {(æ, y, z) =E R° 0 < æ < 1,0 < y < 1,0 < : < x}

A: Given triple integral  ∭Bx2dxdydz, where B=x,y,z∈R3:0≤x≤1,0≤y≤1,0≤z≤x. We have to evaluate…

Q: Evaluate cz dz, where c is |z| = 1 zG-2) Inz %3D

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Q: 3. Obtain the 6.S. sy dx + taydy = 0 xcos

A: We have given equation  xcos2y dx+tany dy=0 xcos2y dx=-tany dy x dx=-tanycos2y dy x dx=-sec2y tany…

Q: 7 2 dx dy y? 3 Evaluate the integral: Jo 98 3 294 3 196 392 3.

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Q: What will be the value of (h, k) in the given DE: * (x – 2y + 1) dx + (4x – 3y – 6) dy = 0 | h = 3,…

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Q: Given f(r, y, z) = In(x² + y? + 2²), show that af, f, s dy? %3D dx² x² + y? + 22

A: The given function is fx,y,z=lnx2+y2+z2........(1) To show: ∂2f∂x2+∂2f∂y2+∂2f∂z2=2x2+y2+z2

Q: Evaluate: / (In(2r – 1) – () + 25) da + 25 ) dx | Limits: [1, 6] Using Trapezoidal, n = 30

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Q: Evaluate /// xe²+y²+z² dV, where E is the portion of the unit ball x2 + y? + z2 < 1 hat lies in the…

A: Given The given integral is ∫∫∫Exex2+y2+z2dV E is the portion of unit ball x2+y2+z2≤1.

Q: %3D 23. f(x, y, z) = 2x + z? subject to x² + y? + 2z? = 25

A: Lagrange's Multipliers: The Lagrange method is used to maximize or minimize a general function…

Q: dy dx If y=e+19 then O 19e+19 O 4er+19 O 57er+19 O 3er+19 2er+19

A: Please see the answer in Step 2

Q: Verify that * ox af dy 2+ ?х ду ду дх ах 22+ 21 ?х ду ду дж 11 olems) for f(x, y)=5x®y -7xy5.

A: Here is the solution of the given problem.  Partial Derivatives.

Q: In(v¤) dædy 6. 15. Calculate ry

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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: 8 Exercise.3 Evaluate y* Va? – y² dy [+hint: assume y² = a?x], [M Check answer: %3D 32

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Q: 9. For the cur ve x = t – In t, y = t + In t, find d²y/dx².

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

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

Q: 5. Use Green's Theorem to evaluate (y – 42) dx – (2+x²y²) dy where C is shown below. y (5,10) 10

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