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Q: 33. Let x² - 4y2 if x + 2y f(x, y) = 2y %3D | 8(x), if x = 2y %3D If fis continuous in the whole…

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Q: What is the domain of the following function? f(z,9) 4-2 - y - In(y - z) + sin(z) +y 24 and y> =)…

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Q: Using the Green's 2nd identity, prove that for 2-D Neumann exterior problems, O(In r) 09 Inr-0 dl .…

A: Consider the Green's second identity, ∭Du∆v-v∆udv=∬∂D=u∂v∂n-v∂u∂nds From the equation consider the…

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A: Diagonalization of the Matrix

Q: Define fi z-> 2 xZ by Ala)l (2,72t1) if xis even 18,0) if t is odd a) Is f injective 2? b) Is f…

A: We have f:Z→z×z Such that fx=x,x+1     if x is evenx,0          if x is odd

Q: 3) Let PIASR ond Thi AxC ßeD. Then his a Anction. Te Ø # 4 B and ø 7b cD then that h'(Y x Y% ]=…

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Q: Q. Oshow that { ante : nENS= Y3 inf %3D B= {x2-3nt! 2n2+1 X GR is Subsd f bounded Find R decide…

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Q: 2.2 If fe R(a) on [a, b] and if Saf da prove that a must be constant on [a, b]. = 0 for every f…

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Q: Q4: 16 u. nin N, then 5 bounded fo belongs t and infinum

A: We define a subsequence  an = Sin(pi/2) + (-1)n = 1 + (-1)n . So, a2n = 2 and a2n - 1 = 0.

Q: Presley tried to prove that AFHJ~ AGHII the following figure, but her proof is wron F 2 G H 4 I What…

A: Check the each statement that it is correct or not than select from the given options.

Q: Find the in tervals on which f hure (il In creasing and decrensing Con cave uP and con cave down and…

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Q: 06) Emd The Taylor Steies of de sivon Junction en Runction with the sadies of cofcesgence gven Domt…

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Q: verif y that the funstio n $(x) VI-x² defined overthe loter val E sati'sfies the coad itions of…

A: Verify rolles theorem

Q: Calculate the trapezoid approximation of o xdx using four subintervals. O T5 = 21.52 O T5 - 23.25 T5…

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Q: a)-What is fof g ofh 3)? fari= gal= bprove f:R¬R fer )=4lis not Surgective and is not injective.

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Q: Let flt.v) = y+3r²e!. Then f satisfies a Lipschitz condition in y with L = 2, given that 1<t<2.…

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Q: 1. Prove with the usual notations that: (a) EV = VE = A (b) A +V =- (c) A= SE Apply the suitable…

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

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: let w- f(xy) and y in Poluy Cordeinate then a+yS %3D or or or 7.

A: Given that, w=fx, y And x and y is in polar form that is, x=rcosθy=rsinθ

Q: Compute the length of the curve r(t) = (21, In(t), r?) over the interval 1 <t < 9. (Use symbolic…

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Q: 2. Do as indicated. if r m, r+1 a. Find all values of m such that g(r)= is continuous everywhere.…

A: Given function is: gx=x+1if x≤mx2if x&gt;m To find all values of m such that given function is…

Q: Use Green's Theorem to evaluate | F. nds, where F = (VE+ 4y, 3r + 4y) C is the boundary of the…

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Q: Use the difinition of error function Prove that: 5(1/₂/2) = 5T let: ere (x) = 33/3324 dt

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Q: Qs Findl the Fauier Ex pensian of Hhe funckian deld in a gula Parul by the weladons Sule Perial by…

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Q: Let A be a positive real number. If the absolute minimum value of f(z) = Ar – 45r³ on [0, 00) occurs…

A: Use the fact that at a point point of minimum value derivative is vanish

Q: V2 Find the ual. af the s-lid romes from rot sing the failion Shoun in Fig- about XAxis withini the…

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Q: 7. let E be the reyion bounded by curve 2+2 in the yex? fint quadant let u xy, Vzy-x d Czry)…

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Q: Let X,X, X be i.i.d. with the following PMF. ...... 25 0.6 ; k = 1 Pk)= 1 0.4 ; k = -1 and let Y =…

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Q: For the Ordinary DE y = f (x, y) to be guaranteed to have a unique solution containing the point…

A: We have to choose correct option where differential equation have unique solution

Q: Consider d Hentiel eps %3D whese, ? is di fential oberator on finction space de fined fox holadary…

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Q: The limit of f (x, y) = yx3 as (x, y) approaches (0,0): %3D x6+v2 O Infinity Doesn't exist O Exists…

A: Evaluate limx,y→0,0 yx3x6+y2

Q: Let f(a) - Compute o o+CIT for the domain 0 aS1. Let ro and ny . %3D • Compute the continuous…

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Q: We hae a theorem that offers conditions when the IVP: x'- f(t, x), x(to) = X , has a unique…

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Q: Find all volves of o,b ond c such that the func Ef×メ goo)= てメー1) 1チxg? 21 if x= 1 is continuous at…

A: Given, gx=ax3+bx2+cx+1x-12,  if x≠12,                               if x=1

Q: Compute the length of the curve r(t) = (21, In(?), r²) over the interval 1 < t < 7. (Use symbolic…

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Q: Considere a função z(x, y) definida implicitamente pela equação sen(y - bz) = -2+x - az, com a e b…

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Q: E R", since the subset {||x – a|| | a E E} of Let E C R™ be non-empty. For -empty and bounded below…

A: Given: Let us consider the given E⊆ℝm. For x∈ℝm, since the subset x-a   a∈E  of ℝ is non-empty and…

Q: A Let f be a piecewise-desined Xiven by the souowing Determine Valves off m and b that makef…

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Q: asuppose flo) ioadifferentialle on the interval E-7, Such that l-1) =4 and fl)=1. 3 fumchorn…

A: Intermediate value theorem and Lagrange mean value theorem

Q: (4) In the figure, Y is compact, BEX*Y. Show that T,(B)s TB) clesed X (T, is the nýuchikn funebran)…

A: Given that Y is compact and B⊂closedX×Y. The objective is to show that, π1B⊂closedX Let's define,…

Q: Use : f(z)-L im $(Z+Az)-f(z) AZ to Prave that -1 when w- I Zキ0

A: Here definition of derivative is given in terms of limit. We have to find the derivative of the…

Q: Given that F) = (yet coso)+(ayé-xsing)5 is conservative on R? (a) Find Potential gGay) Por F. (b)…

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Q: 1. IF One-to-one, Statementr ir true, which the follewng of 1. if f ic Continyous on tr clomain, the…

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Q: Let D be the portion of z = 2x + 5y inside z? + y? = 1, oriented up, and let %3D F (y, z, –2).…

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Q: 2)Evaluate er dA , Ris bounded by y = x2,y 1 3)Evaluate I| Vy2 + 1dA , Ris bounded by x = 4 - y? ,x…

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Q: Let flt.v) = v+3t°e'. -2 -y + 3t2e'. Then f satisfies a Lipschitz condition in y with L = 2, given…

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