-H.. OProve that fcz) =z²,s coutinuous at z=z, O prove that: if Z#20 is dis continnity at Z=Zo, where 2o

Q: 5) Compute J(x²+y?)dxdy, where D is the intersection of c irc les r=2 cosg and =2sing.

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Q: Find J, ()dx Chint:let Z=Jx)

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Q: 3{x.y.2) : x+y²+z's 1024, z2 o}. Let D= Evaluate z dv.

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Q: ax? +b?y +c°z?) a'x+ b°y+c°z xyz abc X y Z. if - prove that b %3D 3. a

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Q: Let S={1/n-1/m: m,n ∈ Z+} What are infS and supS? prove your answers. (you can use the Archimedean…

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Q: Evaluate / (x - 2y + z) ds. S: z = 3 - x, 0sxs 3, 0sys 2

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Q: S', P, (x) dx = | 2, n = 0 10, ne N

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Q: a)show 6) Sop

A: a). It is known that, CovX,Y=EXY-EXEY... (1)EXY|X=X×EY|X...(2)EEX|Y=EX....(3) Now,…

Q: 3. Find the volume of the solid obtained by revolving the region bounded by the curves y = 2x2 + 1…

A: The given curves are: y=2x2+1, y=3-2x2

Q: Po Prove that fcz) = zis coutinuous at z=z. O Prove that. fZキ2。 is dis continnity at z=Zo, where Zn

A: (1) we have to prove that                                                              f(z)=z2 is…

Q: S. Which of the fliowing is te gerl lutin to difiential gu e (a) e+ (b) y (e) yeeoo (4) None of the…

A: Consider the provided question, Given D.E,  y''-4y'+8y=0 We need to find the general solution of the…

Q: Prove that u exy)= (x+a)Ly+b) is the exact Solution of the pOE Ux Uy = 4xy ucy) where (a) and (b)…

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Q: dz; |z – i| = 1 (z – i)3

A: We have to use the Cauchy integral formula to evaluate the following integral ∮ ez2z-ι3dz over the…

Q: a) let-1 ≤x≤ 1. Show that b) Using part (a), find En-1/ 1)", cos(x) c) Find The type of singularity…

A: (a)  Let  fx = x2  x ∈ -1, 1          Since fx = x2 is an even function so the Fourier series of fx…

Q: - H.w oprove thaA Scz) = 2is continuous at z=zo O prove that Z if 斗乙キ2。 is dis continnity at Z=Zo,…

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Q: A car moves from points (0, -1,0) and (0,1,0) through a mountain 0.9 that meets the equation. 0.8…

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Q: [n(n+1)]² 2. Prove: Vn e Z*, Ei i=1 2

A: We prove given statement by Mathematical Induction. Mathematical Induction is a mathematical…

Q: R and r are defined by E(; - 1)(y, – I) VE(*; - 1)² E(Y SSR Sry S,, Syy R? TY r = SST' (1) Show R2 =…

A: Given : R2=SSRSSTr=∑xi-x¯yi-y¯∑xi-x¯2∑(yi-y¯)2r=SxySxxSyy

Q: . Compute CNF (NNF (IMPL FREE ((p V q)->r)>((p>r) V (q→r))))

A: Given, CNFNNFIMPL FREEp∨q→rp→r∨q→r Now, solving the given statement. CNFNNFIMPL…

Q: Hiw Prove that c=z²,'s coutinuous at z=z. O prove that: if Z#Z0 is dis continnity at Z=Zo, where 2o

A: (1) Calculate the RHL and LHL for the function f(z).…

Q: 5. Prove that |xy| = |x|-|y| for x, y eR.

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Q: Let D={(txy.2) : x²ny2sz²s 324, z2 Evaluate z dv.

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Q: Let E Os 0s n, 0s zs 1, 8Vzs rS 8. Compute

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Q: (7) ifa lim has a point that the equalio- prove PCz,y) is above L and only if 3x +2y >4

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Q: 35. Apply the convolution theorem to show that 2e Meu² du = e'erfvi. | (s – 1. (Suggestion:…

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Q: prove: sE121y |Re(z)+| Imcz)l

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Q: In Exercise 5.8, we derived the fact that { Show that Cov(Y₁, Y₂) = 0. Does it surprise you that…

A: We have to show that  Cov(y1,y2)=0 and it surprise that it is zero why or why not

Q: dy then In z is If y = cosh z

A: Without wasting any time, any further, differentiate the RHS to get your answer.

Q: 5. Verify Gauss's theorem for D = {(x, y, z): 0 ≤ z ≤ 9-2²-y²} and F ri+yj + zk.

A: The given problem is to verify the gauss theorem for the given surface 0<z<9-x2-y2 for the…

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