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Q: +++++ ++ + 2 riecononi ni bilw no elV us led (Jq 1) () ++++ dordw go alnoji vas da 1 (1g 1) (b) YOe…

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Q: 7- The function f(z) = z is: a) Analytic on C b) Analytic only at zo = 0 c) Not analytic

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Q: Jc 16.8. For each of the following functions , describe the domain of ana- lyticity and apply the…

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Q: 6. Let A and B be two open subsets of R". Show that their intersection An B is also an open set. 7.…

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Q: 3. Compute the value of F.dr if F = -yi + xj and C is a semicircle from (-1,1) to (1,-1).

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Q: x, y, z)=x²√√x - y² - z²

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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: (c) For any (a, y) E R?, let F(x, y) = (4x - 3y + 1, 3x +4y + 1). Then F is a similarity.

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Q: [1+2p(x-1)+(x-1)² x≤1 x>1 [qx+p -) -) Find the values of q, in terms of p, for which fis continuous…

A: Given:f be a function defined by:a. To find the value of q in terms of p, for which f is…

Q: 1. Let f(x)=x² - x, xeR then f(f(f(v2))) is: -34 + V2. b. 2/2 +34. c. 34+2/2. d. 34– 2/2. e. 2/2 -…

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Q: Let f be a function with 1+ i as the only singular point of it. If 1 +i is a removable singularity…

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Q: 4. Show whether or not f is bijective. Letf : R → R_be defined as f(x) = I피+1 %3D

A: A function f is said to bijective if it is one-one and onto

Q: as Let ĝ +sinh (z?) - ji = 27 where w=f (x,y,2)- %3D Find 2 nd JW and au

A: In the given question we have to find the partial derivatives of with respect to x ,y and z. here we…

Q: if the tangent tangent (x117₁) to the conve of the curve again in (22, 8₂) them proustait me x 1 20…

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Q: (c) Suppose that ø is differentiable. Prove the identity $Vø•n ds |(V*o+ V¢ • Vø) dA

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Q: F.T. 3) If X(t) + y(t) = x (2t - 1) =it W+1 Ans: Yow) = [4+jCW+1)]² X(w) and X (w.) = -j(w+1) e 2…

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Q: 7.2 Give an & - 8 pr at (1 continuous (2x - 2).

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Q: Let fo) -x1 and go) = 3. g0) %3D %3D @ Derermine if the fanctien f:R>R defined by f) is anto…

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Q: 2.5.33. Prove that the image of the function f: R → R , f (x) x2 is the interval [0 ,1) . Do not use…

A: The given function f:ℝ→ℝ f(x)=x21+x2 We have to show the image of the function is  [0,1)

Q: #4) What valwes of c Cif anu) are predicted by the Me an Vae Thearem for the function fex) = (x-32)o…

A: The Mean Value Theorem states that if a function f is continuous on the closed interval [a,b] and…

Q: Prove that f (z) =zz is nowhere analytic

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Q: Shaa thut the graf of lincs iju fins rom F from E Iwhore is a iomasphic wilh Ge(5)

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Q: (*) 1 2x Define F : R x R → R x R as follows: F(x, y) = 2y+7) for all (r, y) ER x R. 3 Prove that F…

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Q: A₁ Let 2 + sinh (2²) - ₁₁ = 27 where w = f (x, y, z)- 1 पुर Find aw дх Jw and Iw > zw. ay dz 3/20

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Q: 5. Find the x-coordinates for all points of discontinuity for f(x)- 「X316, xśl x〉 1 2 c. 1, 32d.…

A: First we check the limits as x approaches to 1 from left side and right side .

Q: If f(x, y) = x²ye*xy, find fx and fyx.

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Q: дz дz Suppose z is a function of r and y and tan(√x + y) = e²². Determine and 3x ду

A: given function tanx+y=ez2

Q: 3. Let fx) = {ax), whire a function. sadafferentiable 10 94x) 1t xa aa glx) and a'cx) Lalwlate the…

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Q: 1.) Which of the following are TRUE about differentiable function: I If rx) exists, then the…

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Q: 2. (8.7.10) Let f (x, y) In y R is the rectangle defined by R {(x, y)|1 < x < e2 and 1 < y < e}.…

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Q: Let f be a function with 1+ i as the only singular point of it. If 1 + i is a removable singularity…

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Q: 8.Prove the following relationships: a) I(X,Y)=H(X)-HOX/Y)

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