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

Q: S (x, y) = sen (r² – 0²) + In(r® + 0), con Vr? + y? A r = = arctan

A: Given that, f(x, y)=sen2r2-θ2+lnrθ+θfor r=x2+y2and θ=arctanyx

Q: Let M(T, y) = sin 2x + 2re +2 %3D and N(x, y) = 2'e + 3y. %3D Select all the statements below that…

A: you can clearly understand if you follow the below solution

Q: evaluate the in! integ ral if u = 16+ ex then e* V T6tex dx = ( Jü cu=(ile %3D

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Q: Let r = xi + yj + zk and let r = ||r||. Prove that

A: As per our guidelines, we are supposed to solve only first question. Kindly repost other question as…

Q: solve the following P.D.E: azu ди + u at u(0, t) = u(1, t) = 0 %3D || (1, 0< x < 1/2 0,1/2 < x < 1…

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Q: -W : By the same way, prove that g Z sinWo sinw.k Z -27 cus Wo +1

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Q: EXERCISE 1 df af. In each of the following, find Əx and (k) f(x, y) = /Ty + VT+ VJ

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Q: The evaluation of S z dx is V4+x2 O In(sece + tan0) + c o - In(sec0 + tan0) + c c In|sece – tan0|+ c…

A: we have to evaluate the following integral .

Q: b? – a? x dx 9. - Proof Prove that 2 a

A: This can be proved using Fundamental theorem of calculus. The second part of the theorem is used.…

Q: F ind the oua gohenegion Aounded ky メ=y,メ=13-が 2 x=18-y (0,9) てっ (,) Une borizontal ilement to firid…

A: The area of the region can be calculated using the formula , where is the curve of the first…

Q: (b) If u = x? cos y+ye», where x= s+2t and y = st, prove that ди 2- ди = (s – 21) (x² sin y – xye" –…

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Q: π/3 So, f²ef/³ t In u tans ds du dt

A: Given problem:-

Q: 10. Given: YX = ZX WX bisects YXZ Prove: AWYX AWZX Statements Reasons

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Q: 二线 2. Given: RS = KL ST = JK RT = JL Prove: ARST= ALKJ T K

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Q: How do I prove this?

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Q: 2) Prove that: d? L„0) = n;(n – 1) %3D dx²

A: Consider the given information: Let Laguerre polynomial is given by, Lnx=∑k=0n(-1)kk!nkxk…

Q: 1. If r = xi + yj + zk and r = |r|, show that (i) div 0, %3D (ii) div (grad ") = n (n + 1) r" - 2…

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Q: O prove that : (2) DO 2x e dx a e +b where a, b >o

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Q: IS T-dist prove o E(T)=0 QvarしT)=て %3D V-2

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Q: H.W: if w=√x2 + y2 + z2, x= erCose, yerSine, z=ee prove that aw/ar = e²r/w and aw/00 = e²0/w

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Q: (10) Without finding T and N, write a(t) in the forma(t) = a-T + ayÑ at t= r(t) =

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Q: E Given: AC= BD D AE = DF ZA = ZD A Prove: ACAE= ABDF F

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Q: I. Given: GH=JR, Hl RT, and Gal H. K %23 %23 Prove: zlezL

A: Given: GH≅JK , HI≅KL , IG¯≅LJ To prove: ∠I≅∠L

Q: (3) Determine whether The following tundions are unitermly continious. Justity your answer Ca) f:…

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Q: 22. Given: 4I 2 Prove: a. AJIG AJZY JG GI b. JY YZ Y

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Q: 27 dr = iex+ h where a, b> 0. Prove that

A: Prove that , ∫-∞∞e2xae3x+bdx=2π33a23b13

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

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Q: (a) Evaluate where c is z = 1 %3D c cos(Tz)

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Q: (a) Let r = ri+ yj + zk and let r = ||r||. Prove that - (1) a

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Q: 6. Use Green's Theorem to evaluate O (y* – xy?) dæ + (2 – a*) dy where C is shown below. y -2 ² +y²…

A: Green's theorem

Q: 1. Find fr fy and fry if f(x,y) = y* + x?y + In xy.

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Q: Express the following tunctrons in the form u+iv f(2)=In (I+z)

A: Solve the given problem.

Q: EX: Find the Z. T. of X(X) = cas wok u(k) Soin

A: Z transform of the function

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

A: We are given a formula as : A≡∀x∀y.p(x,y)∧¬q(x,y) We need to show that A is falsifiable by giving an…

Q: (a) Let r(t) = ti+tej+fk. Find ((1),4 × (?),1) - (1)a tuj

A: First we find out first derivative of r(t) with respect to 't' then find out 2nd derivative and then…

Q: 3. Consider tw o evénts A and B such that Pr(A)= 1/3 and Pr(B)= 1,2. Determine the value of Pr(B 0A)…

A: Given PrA=13 and PrB=12 and A and B are disjoint, that means PrA∩B=PrA×PrB…

Q: 6. Which of the followg quti dy (a) de dy (b) de () +2ry- (e) (4) Al of the above

A: It is given that There are four differential equations option.

Q: 21. xª sen z dz -z' cos z + 3z² sen z + 6z cos z 6 sen z + C %3D

A: see below the answer

Q: D. If z = In(x – y) + tan(x + y), show that Z = Z y XX

A:

Q: assuming that u a (0, ) and 1o olcos u nil sdi no al 11. sin u 12. cos v CED 13. tan u 1 14. tan v

A: given: For the interval , we get cos v = 12 as sin2v+cos2v=1. So,         tan v=sin vcos v=1/21/2=1

Q: The identity S dyd x f, dxdy is %3D O False True

A: We need to check whether the given Identity is True or False.

Q: Vx Sn(l+x*) de 23/2

A: Using the substitution ... Explanation of the solution is given below...

Q: B. Prove by direct proof general. P: Vn e ZE, (n – 1) (n+ 1) e Z,

A: I have solved B; you just need to expand (n-1)(n+1) and then use the fact that square is always…

Q: 1 (aw C. Ifw=f(x.y) and x=1. coso, y=. sino. Prove that

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Q: if z, = (1 – v31) and zz = (V3 + i) by De Movier's theorem z,z– 4% = 1 (cos( +5 + isin +5)

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Q: Ex 6 Show that X -Ca,i) is HOM with y- (1,00) if X and y have the euraal Seibsipace op. af R Hint:…

A: Homeomorphism: Two topological spaces and are said to be homeomorphic if there exists a function…

Q: SA (xit) = S'y St ot) SHL %3D Subject to Con d'tions Detesmine the expre ssion tor u(xst).

A: Given partial differential equation is                                 ∂∂tux, t=∂2∂x2ux, t…

Q: If p(x, y, z) = x²z + ey/x, evaluate grad op at the point (1, 0, -1).

A: The function is φ(x, y, z)=x2z+ey/x

Q: QR I RS and UV 1 TÚ. Construct a proof that ZQRS = ZTUV.

A: First, we sketch the situation roughly  We have to prove:

Q: The IHiplicative in verse of 2° tX -I in Zs [x] /is; mu d. nune of

A: Ring Theory.